Question

question 15
what is the slope of the line that contains the points (-1, -1) and (3, 15)?
a. -4
b. $\frac{1}{4}$
c. 4
d. $\frac{1}{4}$

question 16
the slope of the line passing through points (-6, 3) and (-6, 39) is ______.
a. positive
b. zero
c. undefined
d. negative

question 17
what is the slope of the line given by the equation $y = -7x$?
a. $\frac{1}{7}$
b. 7
c. $-\frac{1}{7}$
d. -7

question 18
if $\overline{ab}$ is parallel to $\overline{cd}$ and the slope of $\overline{cd}$ is -5, what is the slope of $\overline{ab}$?
a. 5
b. $\frac{1}{5}$
c. $-\frac{1}{5}$
d. -5

question 19
what is the y-intercept of the line given by the equation $y = 8x + 75$?
a. (0, 75)
b. (0, -8)
c. (0, -75)
d. (0, 8)

Explanation:

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Question 15

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Substitute points $(-1,-1),(3,15)$

$m = \frac{15 - (-1)}{3 - (-1)} = \frac{16}{4} = 4$

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Question 16

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Substitute points $(-6,3),(-6,39)$

$m = \frac{39 - 3}{-6 - (-6)} = \frac{36}{0}$

Step3: Evaluate undefined division

Division by 0 is undefined.

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Question 17

Step1: Recall slope-intercept form

$y = mx + b$, where $m$ = slope

Step2: Match with given equation $y=-7x$

The coefficient of $x$ is $-7$, so slope $m=-7$

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Question 18

Step1: Recall parallel line slope rule

Parallel lines have equal slopes.

Step2: Apply rule to given slope

Slope of $\overline{CD}=-5$, so slope of $\overline{AB}=-5$

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Question 19

Step1: Recall slope-intercept form

$y = mx + b$, where $(0,b)$ is y-intercept

Step2: Match with given equation $y=8x+75$

Here $b=75$, so y-intercept is $(0,75)$

Answer:

Question 15: C. 4
Question 16: C. undefined
Question 17: D. -7
Question 18: D. -5
Question 19: A. (0, 75)