8. an elevator rises steadily up a skyscraper. after 4 s it is 33 m above the ground. two seconds later it is 47 m above the ground. which equation models its height, y, with respect to time, x? a y - 33 = -7(x - 4) b y - 47 = -7(x - 2) c y - 33 = 7(x - 4) d y + 33 = 7(x + 4) 9. what are the x - and y - intercepts of the graph of 5x + 8y = 20? graph the equation. 10. jake needs to buy 120 beverages for a party. what equation, in standard form, determines the numbers of 8 - packs of juice x and 12 - packs of water y that jake can buy? 11. for the situation in item 10, select all the ordered pairs that represent combinations of packs of juice and packs of water that jake can buy. a (0, 10) b (12, 2) c (-2, 11) d (7 1/2, 5) e (30, -10) 12. graph the equation 4x + 8y = 16. what is the slope of the graph? 13. what is the equation in slope - intercept form of the line that passes through the point (-0.5, 7) and is parallel to the graph of y = -8x - 2? 14. select all the equations that represent lines that are perpendicular to the graph of 6x + 18y = 5. a y = 3x - 10 b x = 3 c y + 6 = 3(x - 15) d 3x + 9y = 8 e 2x - 3y = 5 15. (overline{ab}) of rectangle abcd passes through the point (2, 0) and is perpendicular to the graph of y = (\frac{1}{4})x - 3. (overline{cd}) is parallel to (overline{ab}) and passes through point (-1, 6). select the equation in slope - intercept form of the line that includes (overline{cd}). a y = (\frac{1}{4})x + 2 b y = -(\frac{1}{4})x + 2 c y = -4x + 2 d y = 4x + 2

Question

Accepted Answer

### 8.
# Explanation:
## Step1: Calculate the slope
The elevator is at $y_1 = 33$ m at $x_1=4$ s and at $y_2 = 47$ m at $x_2=(4 + 2)=6$ s. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{47-33}{6 - 4}=\frac{14}{2}=7$.
Using the point - slope form of a line $y - y_1=m(x - x_1)$, with the point $(x_1,y_1)=(4,33)$ and $m = 7$, we get $y-33 = 7(x - 4)$.
# Answer:
C. $y - 33=7(x - 4)$

### 9.
# Explanation:
## Step1: Find the x - intercept
Set $y = 0$ in the equation $5x+8y=20$. Then $5x=20$, so $x = 4$.
## Step2: Find the y - intercept
Set $x = 0$ in the equation $5x+8y=20$. Then $8y=20$, so $y=\frac{20}{8}=\frac{5}{2}=2.5$.
# Answer:
x - intercept: $4$
y - intercept: $2.5$

### 10.
# Explanation:
Each 8 - pack of juice has 8 beverages and each 12 - pack of water has 12 beverages. The total number of beverages is 120. So the equation in standard form is $8x+12y=120$.
# Answer:
$8x + 12y=120$

### 11.
# Explanation:
The equation from item 10 is $8x+12y=120$, which can be rewritten as $2x + 3y=30$ or $y=-\frac{2}{3}x + 10$.
## Step1: Check option A
For $(x = 0,y = 10)$, $8	imes0+12	imes10=120$.
## Step2: Check option B
For $(x = 12,y = 2)$, $8	imes12+12	imes2=96 + 24=120$.
## Step3: Check option C
For $(x=-2,y = 11)$, $8	imes(-2)+12	imes11=-16 + 132 = 116
eq120$.
## Step4: Check option D
For $(x = 7.5,y = 5)$, $8	imes7.5+12	imes5=60+60 = 120$.
## Step5: Check option E
For $(x = 30,y=-10)$, $8	imes30+12	imes(-10)=240-120 = 120$.
# Answer:
A. $(0,10)$
B. $(12,2)$
D. $(7.5,5)$
E. $(30,-10)$

### 12.
# Explanation:
Rewrite the equation $4x + 8y=16$ in slope - intercept form $y=mx + b$ (where $m$ is the slope and $b$ is the y - intercept). First, solve for $y$: $8y=-4x + 16$, so $y=-\frac{4}{8}x+2=-\frac{1}{2}x + 2$. The slope $m=-\frac{1}{2}$.
# Answer:
$-\frac{1}{2}$

### 13.
# Explanation:
Parallel lines have the same slope. The line $y=-8x - 2$ has a slope of $m=-8$.
Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(x_1,y_1)=(-0.5,7)$ and $m=-8$, we have $y - 7=-8(x+0.5)$. Expand it: $y-7=-8x-4$, so $y=-8x + 3$.
# Answer:
$y=-8x + 3$

### 14.
# Explanation:
First, rewrite the equation $6x+18y=5$ in slope - intercept form: $18y=-6x + 5$, so $y=-\frac{6}{18}x+\frac{5}{18}=-\frac{1}{3}x+\frac{5}{18}$.
The slope of a line perpendicular to it has a slope $m$ such that $m	imes(-\frac{1}{3})=-1$, so $m = 3$.
## Step1: Check option A
The slope of $y = 3x-10$ is $3$.
## Step2: Check option B
The line $x = 3$ is a vertical line, not perpendicular (since the given line is not horizontal).
## Step3: Check option C
Rewrite $y + 6=3(x - 15)$ as $y=3x-45 - 6=3x-51$, slope is 3.
## Step4: Check option D
Rewrite $3x+9y=8$ as $9y=-3x + 8$, $y=-\frac{3}{9}x+\frac{8}{9}=-\frac{1}{3}x+\frac{8}{9}$, slope is $-\frac{1}{3}$.
## Step5: Check option E
Rewrite $2x-3y=5$ as $-3y=-2x + 5$, $y=\frac{2}{3}x-\frac{5}{3}$, slope is $\frac{2}{3}$.
# Answer:
A. $y = 3x-10$
C. $y + 6=3(x - 15)$

### 15.
# Explanation:
The line $y=\frac{1}{4}x-3$ has a slope of $\frac{1}{4}$. A line perpendicular to it has a slope $m$ such that $m	imes\frac{1}{4}=-1$, so $m=-4$.
Since $\overline{CD}$ is parallel to $\overline{AB}$ (which is perpendicular to $y=\frac{1}{4}x - 3$), the slope of $\overline{CD}$ is also $-4$.
Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(x_1,y_1)=(-1,6)$ and $m=-4$, we get $y - 6=-4(x + 1)$. Expand it: $y-6=-4x-4$, so $y=-4x+2$.
# Answer:
C. $y=-4x + 2$

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QUESTION IMAGE

Question

Explanation:

8.

Step1: Calculate the slope

Step1: Find the x - intercept

Step2: Find the y - intercept

Answer:

9.