Question 1

Given the points $(-3, -3)$ and $(6, 3)$, what is the slope $m$ of the line passing through these points?

Accepted Answer

$m = \dfrac{3 - (-3)}{6 - (-3)} = \dfrac{6}{9} = \dfrac{2}{3}$

Question 2

What is the equation of the line in slope-intercept form ($y = mx + b$) that passes through $(-3, -3)$ and $(6, 3)$?

Accepted Answer

$y = \dfrac{2}{3}x - 1$

Question 3

Which of the following is the equation of the line in point-slope form passing through $(-3, -3)$ with slope $\dfrac{2}{3}$?

Accepted Answer

$y + 3 = \dfrac{2}{3}(x + 3)$

Question 4

A line has a slope of $\dfrac{1}{3}$ and a $y$-intercept of $-5$. What is its equation in slope-intercept form?

Accepted Answer

$y = \dfrac{1}{3}x - 5$

Question 5

For the line $y = \dfrac{1}{3}x - 5$, what is the $x$-intercept?

Accepted Answer

$x = 15$

Question 6

Which of the following best describes the graph of the line $y = \dfrac{2}{3}x - 1$?

Accepted Answer

It rises from left to right and crosses the $y$-axis at $-1$.

Question 7

If a line passes through $(6, 3)$ and has a slope of $\dfrac{2}{3}$, what is its equation in point-slope form?

Accepted Answer

$y - 3 = \dfrac{2}{3}(x - 6)$

Question 8

A chemical reaction's temperature $T$ (in $^\circ$C) increases linearly with time $t$ (in minutes). At $t = 0$, $T = 20$, and at $t = 10$, $T = 50$. What is the equation relating $T$ and $t$?

Accepted Answer

$T = 3t + 20$

Question 9

A patient’s blood sugar level $B$ (in mg/dL) decreases linearly after taking insulin. If $B = 180$ at $t = 0$ minutes and $B = 120$ at $t = 30$ minutes, what is the rate of change of $B$ with respect to $t$?

Accepted Answer

$-2$ mg/dL per minute

Question 10

A taxi charges a flat fee of $\$4$ plus $\$2$ per mile. Which equation models the total cost $C$ for $m$ miles?

Accepted Answer

$C = 2m + 4$

Question 11

A line passes through $(0, -5)$ and has a slope of $\dfrac{1}{3}$. What is the $y$-coordinate when $x = 6$?

Accepted Answer

$-3$

Question 12

Which of the following points lies on the line $y = \dfrac{2}{3}x - 1$?

Accepted Answer

$(3, 1)$

Question 13

If the $x$-intercept of a line is $x = 15$ and the $y$-intercept is $-5$, what is the slope of the line?

Accepted Answer

$\dfrac{1}{3}$

Question 14

A line has the equation $y = mx + b$. If $m > 0$ and $b < 0$, which quadrant does the line cross the $y$-axis?

Accepted Answer

Quadrant IV

Question 15

A business’s profit $P$ (in dollars) is modeled by $P = 50x - 200$, where $x$ is the number of units sold. What is the break-even point (where $P = 0$)?

Accepted Answer

$x = 4$

Equations of Lines and Their Graphs

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