微积分
极限、导数、最优化与函数性质。
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3) $y = 3|x - 2| + 3$
The graph is a V-shaped absolute value function with vertex at $(2, 3)$, passing through points $(1, 6)$, $(3, 6)$, and $(0, 9)$, opening upwards with a slope of $3$ for $x>2$ and…
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2) $y=(x^2 - 8x) - 10$
In vertex form, \(y=(x - 4)^{2}-26\)
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find the most general antiderivative or indefinite integral.\\(\\int \\…
$5\sec x + 3\tan x + C$ (where $C$ is an arbitrary constant)
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how did consumers weaken the economy in the late 1920s? ○ consumers onl…
B. Consumers bought too many goods they could not afford.
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3. select all descriptions that accurately define the meaning of a func…
a. Every x-coordinate has one unique y-coordinate. d. Every independent variable has one unique dependent variable. e. Set of ordered pairs.
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divide. express the quotient as a fraction in simplest form. 4 ÷ 3/8 = …
32/3
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mfm2p name: _______________ date: _____________ 5. graph the following …
The parabola has vertex $(-2, -9)$, x-intercepts $(-5, 0)$ and $(1, 0)$, y-intercept $(0, -5)$. When graphed, it is an upward-opening parabola passing through these key points on …
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what is the value of $3\\frac{1}{3} \\div \\frac{2}{3}$? show your work…
\(5\)
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if $f(x)=3x^2 + 12x + 9$, what are the coordinates of the vertex? a. $(…
c. (-2, -3)
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for the quadratic function $f(x)=x^2 - 10x + 25$, what is the $y$-coord…
b. 0
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given the quadratic function $f(x) = -4x^2 + 8x - 1$, what is the maxim…
c. 3
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the maximum value of the function $f(x) = -2x^2 + 4x + 5$ occurs at wha…
b. 7
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lessons 2.1-2.2 review & refresh complete the equation. identify the pr…
1. $8$, Propiedad conmutativa de la suma 2. $2$, Propiedad asociativa de la multiplicación 3. $1$, Elemento identidad de la multiplicación 4. $0$, Elemento identidad de la suma 5.…
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for what value of x is \\(\\cos(x) = \\sin(14^\\circ)\\), where \\(0^\\…
A. 76°
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lesson 8.6 extra practice subtract. 1. $5\\frac{1}{2} - 2\\frac{1}{4} =…
1. $3\frac{1}{4}$ 2. $2\frac{1}{6}$ 3. $3\frac{3}{4}$ 4. $\frac{7}{10}$ 5. $3\frac{1}{4}$ 6. $3\frac{7}{8}$ 7. $7\frac{17}{24}$ 8. $7\frac{1}{9}$ 9. $7\frac{13}{24}$ 10. $4\frac{1…
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lesson 8.5 extra practice add. 1. $3\\frac{1}{2} + 2\\frac{1}{4} = \\un…
1. $5\frac{3}{4}$ 2. $11\frac{1}{2}$ 3. $9\frac{1}{10}$ 4. $6\frac{7}{12}$ 5. $6\frac{5}{8}$ 6. $10\frac{3}{4}$ 7. $8\frac{5}{9}$ 8. $9\frac{5}{24}$ 9. $2\frac{17}{20}$ 10. $4\fra…
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write an equation of the line below. try again
\(y = -3x\)
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write an equation of the line below. your answer
\(y = 4x - 1\)
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what is the absolute value of 2? 0 2 -2 rewatch submit
$\boldsymbol{2}$ (the option with the value 2)
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practice: 9. identify the slope and y-intercept of $y = -3x + 7$.
Slope: $-3$ y-intercept: $7$ (or the point $(0, 7)$)
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what is the effect of replacing the graph of the function $f(x)=x^3 - 2…
The graph of $f(x)$ shifts down by 3 units.
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what does the transformation $f(x) \\mapsto 4f(x)$ do to the graph of $…
stretches it vertically
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what does the transformation $f(x) \\mapsto -f(x)$ do to the graph of $…
reflects it across the x-axis
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what does the transformation $f(x) \\mapsto f(2x)$ do to the graph of $…
shrinks it horizontally
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what does the transformation $f(x) \\mapsto \\frac{1}{9}f(x)$ do to the…
shrinks it vertically
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what does the transformation $f(x) \\mapsto f(x - 4) + 6$ do to the gra…
translates it 4 units right and 6 units up
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what does the transformation $f(x) \\mapsto f(x - 8) - 3$ do to the gra…
translates it 8 units right and 3 units down
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what does the transformation $f(x) \\mapsto f(x - 4)$ do to the graph o…
translates it 4 units right
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what does the transformation $f(x) \\mapsto f(x - 10)$ do to the graph …
translates it 10 units right
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practice: 7. find the slope of a line that rises 8 units and runs 4 uni…
1. For question 7: The slope is $2$ 2. For question 8: The slope of a horizontal line is $0$, and it is a zero slope (horizontal line with no vertical change).
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use inductive reasoning to predict the next three numbers in the patter…
768, -3072, 12288
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three skills that can help you choose abstinence are setting clear limi…
avoiding high-pressure situations
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reba makes 3d - printed toys and sells them online. she predicts that i…
\( 7.5 \)
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graph the line using the slope and y-intercept. graph the line through …
The line is graphed by first plotting the y - intercept \((0,1)\), then using the slope \(-5=\frac{-5}{1}\) to find another point (e.g., \((1,-4)\)) and drawing a straight line th…
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what is a good strategy to take when setting limits for expressing sexu…
Consider the values that you hold.
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match the exponential functions ( y = 2^{\frac{x}{2}} ), ( y = 2^{2x} )…
To solve the problem of matching the exponential functions to their graphs, we analyze each function's key features (y - intercept, growth rate) and compare them with the graphs: …
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practice question 1 of 3 attempt 1 of 3 which feature characterizes a g…
C. Can be difficult to test (assuming the options are labeled A, B, C, D with A: Begins with an observation of a specific phenomenon, B: Limited scope, C: Can be difficult to test…
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part e: using substitution, evaluate the following expressions with the…
1. $0.625$ 2. $288$ 3. $11$ 4. $1$ 5. $72$ 6. $11.96$
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6 what is a creole language? a simplified, limited non - native languag…
C. A language that develops into a new combined language with native speakers.
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2 what is a pidgin language? a a language that develops into a new comb…
C. Simplified, limited non - native language used by two people that speak two different languages
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which graph shows the solution to the system of linear equations? y = 3…
The graph that shows two lines intersecting at the point $(2, 3)$, with one line having a slope of 3 and y-intercept at $(0, -3)$, and the other line having a slope of 1 and y-int…
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determine each feature of the graph of the given function. f(x) = (-2(x…
# of Horizontal Asymptotes: One # of Holes: One # of Vertical Asymptotes: None # of x-intercepts: None # of y-intercepts: One
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11. $x^5 = -112$
\( x\approx - 2.47 \) (or \( x = \sqrt[5]{-112}\))
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math 30 pre - calculus chapter 10 review name: ella answer all question…
\(6\) ### Part b: \((g - f)(4)\)
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12. 1.86^1
\(3.4596\)
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the parent function $y = \\sqrt3{x}$ and a transformed function $y = \\…
The graph of the parent function \( y=\sqrt[3]{x} \) is translated \(\boldsymbol{1}\) unit(s) right and \(\boldsymbol{3}\) unit(s) up to graph the transformed function \( y=\sqrt[…
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square root functions and equations which function represents the graph…
\( y=\sqrt[3]{x - 3}+3 \) (the first option)
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use the given information to write the equation of the line in point - …
The first box: \(-2\), the second box: \(-1\), the third box: \(1\) So the equation is \( y-(-2)=-1(x - 1) \), filling in the boxes: \( y-\boxed{-2}=\boxed{-1}(x-\boxed{1}) \)
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12) if $y = \\frac{1 - x}{2x + 1}$, then $\\frac{dy}{dx} =$
\( \frac{-3}{(2x + 1)^2} \)
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use the number selector to fill in the correct answer for each equation…
160
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11) $y = 3 \\sin^2 2x$, $\\frac{d^2 y}{dx^2} = $
\(24\cos4x\)
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to input your answer. the model represents 84 ÷ 4. what is 84 ÷ 4? 84 ÷…
21
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use the calculator below to approximate \\(\\sqrt{32}\\) as a decimal t…
$\sqrt{32} \approx 5.66$
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what is $-2.3 - \\left(4.5 - 3\\frac{1}{2}\ ight)$? -3.3 -1.3 -10.3 2.3
-3.3
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what is $-8.64 \\div -0.024$? 360, -360, 36, -36
360
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comparing print and media quick check before deciding on a medium to us…
compare the strengths and limitations of each medium
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match each polynomial function to its graph. $f(x) = x^3 - 21x^2 + 147x…
The left graph crosses the x-axis at $x=-3$, matching this. ## Step3: Match functions to graphs $f(x)$ → right graph; $g(x)$ → left graph.
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solve this system of equations. y = -4x + 2 y = 3x - 5 use the sketch t…
The solution is \( x = 1 \), \( y = -2 \) (or the ordered pair \( (1, -2) \)).
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select all the correct answers. fatima is a well - reviewed author in t…
B. copyright infringement, and (if there's another, but based on analysis, only B is correct? No, the problem says "select all", so maybe two. Wait, maybe I misread. Let's check a…
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drag the steps used to evaluate the expression to arrange them in the c…
1. Simplify the power 2. Add 3. Divide 4. Subtract
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match each polynomial function to its graph. $f(x) = -2x^{2}$ $g(x) = -…
Left graph: $f(x) = -2x^2$; Right graph: $g(x) = -x^2 + 1$
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here is a graph that represents one equation in a system of equations. …
$y = -\frac{1}{4}x + 2$ (or equivalent forms like $4y=-x + 8$ or $x + 4y=8$)
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solve this system of equations. y = 4x + 8 y = 2x + 16 use the sketch t…
The solution to the system is \( x = 4 \), \( y = 24 \) (or the ordered pair \( (4, 24) \))
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match each polynomial function to its graph. $f(x) = x^4 + 12x^3 + 54x^…
$f(x)=(x+3)^4$ matches the left graph; $g(x)=(x^2+1)(x^2+4)$ matches the right graph.
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match each polynomial function to its graph. $f(x) = -x^4 - 5x^2 - 4 = …
Left graph: \(f(x) = -x^4 - 5x^2 - 4\); Right graph: \(g(x) = -x^4 + 4x^3 - 6x^2 + 8x - 8\)
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which equation represents the gr (0, 3) (3, 2) -5 -4 -3 -2 -1 0 1 2 3 4…
$y = -\frac{1}{3}x + 3$
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what is a state of work that becomes free for use 50 to 100 years after…
C. Public domain
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what is the slope of the line represented by the equation $y = -\frac{1…
A. $-\frac{1}{2}$
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drag the points to create a graph to determine x- and y-values that mak…
\((3, 1)\)
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the point where the graphs of two equations intersect has a y-coordinat…
\(y=x + 1\)
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introduction 1. ______ ______ are personality - specific traits and can…
1. Work styles 2. Teamwork 3. team 4. active 5. part 6. body; interruptions; listen; notes; your turn
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c. $f(x) = (x^2 + 1)(x - 2)(x - 3)$ degree: _______________ leading coe…
Degree: \( \boldsymbol{4} \) Leading Coefficient (+ or -): \( \boldsymbol{+} \) Zeros: \( \boldsymbol{x = 2,x = 3,x = i,x=-i} \) (real zeros: 2, 3; complex zeros: \( i,-i \)) Mult…
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name period in a parliamentary system, who actually votes for the head …
Lawmakers ### 2. Explain how the Presidential system uses checks and balances
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problem 2 drag the points to create a graph to determine ( x )- and ( y…
The solution is \( x = 3 \) and \( y = 1 \), so the point is \( (3, 1) \).
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what does the sentence “...her friendships were landmines, waiting to e…
Jada feels unsafe and anxious in her relationships.
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7. the dawes plan was created to a. rebuild european economies b. reduc…
7. A. rebuild European economies 8. D. reduce car prices 9. B. connected Americans to shared culture 10. C. increase consumer spending 11. C. supply-side economics 12. B. cooperat…
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4÷3 = \\frac{4}{3} = \\square \\frac{\\square}{\\square}
$4\div3 = \frac{4}{3}=1\frac{1}{3}$ So the boxes should be filled with 1, 1, and 3 (from left to right, top to bottom in the mixed number part).
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dividing scientific notation 1) $(3 \\times 10^{-2}) \\div (0.3 \\times…
1. $2.31 \times 10^2$ 2. $6 \times 10^3$ 3. $1.09 \times 10^2$ 4. $3 \times 10^1$ 5. $9 \times 10^{-5}$ 6. $3.9 \times 10^{-8}$ 7. $7.4 \times 10^{-2}$ 8. $3.20 \times 10^9$ 9. $1…
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the average rate of change for the interval $2\\leq x \\leq 3.5$ is
$-4.75$ (rounded to two decimal places, or $-4.749$ for more precision)
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learning target 2: i can represent mathematical situations as well as r…
a) 1571 b) 45
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using the scale on the graph. the average rate of change for $-3 \\leq …
$7.36$
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evaluate. 14 + 3 |-4 - (-15)|
\(47\)
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the average rate of change for 0≤x≤1.5 is \\boxed{}. the average rate o…
For $0 \leq x \leq 1.5$: $4$ For $1 \leq x \leq 2$: $6$
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3. a housing code limits a studio apartment occupancy to no more than t…
b. \( n \leq 2 \)
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transformations of the quadratic parent function translations possible …
The graph of \( f \) is translated 5.4 units \(\boldsymbol{\text{left}}\) and 2.5 units \(\boldsymbol{\text{down}}\) to create the graph of the function \( g \).
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1. what is the correct graph for the inequality $3 \\geq x$? a. open ci…
c. Closed circle at 3 with shading to the left
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transformations of the quadratic parent function translations if ( f(x)…
A. \(g(x)=f(x + 4)-1\)
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lesson 5-2 radical expressions quick review the product property of squ…
To solve these problems, we'll address a few of them step by step. Let's start with simplifying radical expressions (Lesson 5-2) and then move to exponential functions (Lesson 5-3…
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d. where was isaac 3 hours after school ended? 6. lexie completed an 18…
Isaac was 18 miles from the starting point (or at the end of the triathlon) 3 hours after school ended.
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find the value of \\(\\sqrt3{1000}\\).
10
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find the slope of the line graphed below.
\(1\)
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find the slope of the line graphed below.
\(1\)
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determine the domain on which the following graph of f(x) is negative.
The domain is $(-\infty, -3) \cup (1, \infty)$
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determine the domain on which the following graph of f(x) is negative.
The domain is $(-\infty, -3) \cup (1, \infty)$
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do these problems in your head. use paper only for the problems that yo…
$56 \div 0.8 = 70$ $2.7 \div 9 = 0.3$ $1.4 \div 0.2 = 7$ $1800 \div 0.9 = 2000$ $0.18 \div 0.6 = 0.3$
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q(x)=x²+5 r(x)=√(x+7) find the following. (r∘q)(2) = (q∘r)(2) =
\((r \circ q)(2)=\boldsymbol{4}\) \((q \circ r)(2)=\boldsymbol{14}\)
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k. \\log_{10} 4 + \\log_{10} x = 2
$x = 25$
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k. \\log_{10} 4 + \\log_{10} x = 2
$x = 25$
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write the equation of this line in slope - intercept form. write your a…
$y=\frac{2}{3}x+6$
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write the equation of the line in fully simplified slope-intercept form.
$y=-\frac{7}{4}x+7$