Question 1

Given the points $(-4, -1)$ and $(4, 11)$, what is the slope $m$ of the line passing through them?

Accepted Answer

$m = \frac{11 - (-1)}{4 - (-4)} = \frac{12}{8} = \frac{3}{2}$

Question 2

What is the point-slope form of the equation of the line passing through $(-4, -1)$ and $(4, 11)$?

Accepted Answer

$y + 1 = \frac{3}{2}(x + 4)$

Question 3

Convert the point-slope form $y + 1 = \frac{3}{2}(x + 4)$ to slope-intercept form.

Accepted Answer

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

Question 4

Which of the following is the correct slope-intercept form for the line passing through $(-4, -1)$ and $(4, 11)$?

Accepted Answer

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

Question 5

A line passes through $(-4, -1)$ and $(4, 11)$. What is the $y$-intercept of this line?

Accepted Answer

$5$

Question 6

If a line passes through $(-4, -1)$ and $(4, 11)$, what is the equation of the line in point-slope form using the point $(4, 11)$?

Accepted Answer

$y - 11 = \frac{3}{2}(x - 4)$

Question 7

Which of the following points also lies on the line passing through $(-4, -1)$ and $(4, 11)$?

Accepted Answer

$(0, 5)$

Question 8

A chemical reaction produces a linear increase in temperature over time. If the temperature is $-1^\circ$C at $t = -4$ minutes and $11^\circ$C at $t = 4$ minutes, what is the equation relating temperature $T$ to time $t$?

Accepted Answer

$T = \frac{3}{2}t + 5$

Question 9

If the equation of a line is $y = \frac{3}{2}x + 5$, what is the value of $x$ when $y = 17$?

Accepted Answer

$8$

Question 10

A medical researcher tracks the growth of bacteria in a petri dish. The population is $-1$ at $t = -4$ hours and $11$ at $t = 4$ hours. Assuming linear growth, what is the population at $t = 0$?

Accepted Answer

$5$

Question 11

Which of the following is NOT a valid way to write the equation of the line passing through $(-4, -1)$ and $(4, 11)$?

Accepted Answer

$y - 4 = \frac{3}{2}(x - 11)$

Question 12

If a line has equation $y = \frac{3}{2}x + 5$, what is the change in $y$ as $x$ increases from $-4$ to $4$?

Accepted Answer

$12$

Question 13

Which of the following statements about the line passing through $(-4, -1)$ and $(4, 11)$ is true?

Accepted Answer

The slope is positive and the line rises from left to right.

Question 14

If the equation of a line is $y = \frac{3}{2}x + 5$, what is the $x$-intercept?

Accepted Answer

$x = -\frac{10}{3}$

Question 15

A line passes through $(-4, -1)$ and $(4, 11)$. If $y$ represents profit in dollars and $x$ represents time in months, what is the average rate of change of profit per month?

Accepted Answer

$\frac{3}{2}$ dollars/month

Equations of a Line: Point-Slope and Slope-Intercept Forms

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