Question

y = mx + b. graph the following. determine the point where the lines intersect!

first set of equations and graph:
$y = -x - 1$
$y = x - 3$
graph

second set:
$y = \frac{1}{2}x - 1$
$y = -\frac{3}{4}x + 4$
graph

third set:
$y = -x + 1$
$y = 4$
graph

fourth set:
$y = -\frac{1}{2}x + 4$
$x = 4$
graph

fifth set:
$y = -4x - 2$
$y = -x + 1$
graph

sixth set:
$y = \frac{1}{2}x + 3$
$y = -\frac{5}{2}x - 3$
graph

1. is the point (-3, 5) a solution to $y = \frac{2}{3}x + 7$?

show work!

1. graph a line with

$x$-intercept = (-5,0)
$y$-intercept = (0, 3)
graph

1. given $f(x) = \frac{3}{4}x - 6$

find $f(8) = $
find $x$ so that $f(x) = 18$

1. given $h(x) = \frac{2}{3}x - 4$ fill in the table.

$x$	$h(x)$
-3
	24

1. solve for $y$ then state the slope of the line. $4x - 3y = 15$

$m = $

Explanation:

Top Section: Intersection Points of Lines

For each pair of lines, set equations equal and solve.

Step1: Set equations equal

$y=-x-1$; $y=x-3$
$-x-1=x-3$

Step2: Solve for $x$

$-2x=-2 \implies x=1$

Step3: Find $y$

$y=1-3=-2$
---

Step1: Set equations equal

$y=\frac{1}{2}x-1$; $y=-\frac{3}{4}x+4$
$\frac{1}{2}x-1=-\frac{3}{4}x+4$

Step2: Solve for $x$

$\frac{2}{4}x+\frac{3}{4}x=5 \implies \frac{5}{4}x=5 \implies x=4$

Step3: Find $y$

$y=\frac{1}{2}(4)-1=1$
---

Step1: Set equations equal

$y=-x+1$; $y=4$
$-x+1=4$

Step2: Solve for $x$

$-x=3 \implies x=-3$
---

Step1: Set equations equal

$y=-\frac{1}{2}x+4$; $x=4$

Step2: Find $y$

$y=-\frac{1}{2}(4)+4=2$
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Step1: Set equations equal

$y=-4x-2$; $y=-x+1$
$-4x-2=-x+1$

Step2: Solve for $x$

$-3x=3 \implies x=-1$

Step3: Find $y$

$y=-(-1)+1=2$
---

Step1: Set equations equal

$y=\frac{1}{2}x+3$; $y=-\frac{5}{2}x-3$
$\frac{1}{2}x+3=-\frac{5}{2}x-3$

Step2: Solve for $x$

$3x=-6 \implies x=-2$

Step3: Find $y$

$y=\frac{1}{2}(-2)+3=2$

Step1: Substitute $x=-3$ into equation

$y=\frac{2}{3}(-3)+7$

Step2: Calculate right-hand side

$y=-2+7=5$

Plot the x-intercept $(-5,0)$ and y-intercept $(0,3)$ on the grid, then draw a straight line connecting the two points.

Answer:

1. $(1, -2)$
2. $(4, 1)$
3. $(-3, 4)$
4. $(4, 2)$
5. $(-1, 2)$
6. $(-2, 2)$

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Question 8