Q: Which of the following tables could represent a linear function?

$\begin{array}{c|c} x & f(x) \\ 0 & 2 \\ 1 & 5 \\ 2 & 8 \\ 3 & 11 \end{array}$

Question 1

Which of the following equations represents a linear function?

Accepted Answer

$f(x) = 5x - 7$

Question 2

Given the points $(2, 5)$ and $(6, 13)$, what is the slope of the line passing through them?

Accepted Answer

$m = 2$

Question 3

Which of the following lines is perpendicular to the line $y = -\dfrac{1}{3}x + 2$?

Accepted Answer

$y = 3x - 1$

Question 4

A certain bacteria population doubles every hour. Which of the following functions best models the number of bacteria after $t$ hours?

Accepted Answer

$B(t) = 2^t$

Question 5

Find the $y$-intercept of the line with equation $4x - 2y = 8$.

Accepted Answer

$(0, -4)$

Question 6

Suppose the cost $C(a)$ of planting seeds is given by $C(a) = 3000 + 200a$, where $a$ is the number of acres planted. What does the number 200 represent in this context?

Accepted Answer

The cost per acre to plant seeds

Question 7

Which of the following tables could represent a linear function?

Accepted Answer

$\begin{array}{c|c} x & f(x) \ 0 & 2 \ 1 & 5 \ 2 & 8 \ 3 & 11 \end{array}$

Question 8

If a line passes through the points $(1, 4)$ and $(5, 12)$, what is the equation of the line in slope-intercept form?

Accepted Answer

$y = 2x + 2$

Question 9

Which of the following best describes the slope of a horizontal line?

Accepted Answer

Zero

Question 10

Given the equation $y = -3x + 7$, what is the $x$-intercept?

Accepted Answer

$(\dfrac{7}{3}, 0)$

Question 11

A runner starts 4 miles from home and runs toward home at a constant rate of 1 mile every 8 minutes. Which equation models the distance $d(t)$ from home after $t$ minutes?

Accepted Answer

$d(t) = 4 - \dfrac{1}{8}t$

Question 12

Which of the following lines is parallel to the line $y = 5x - 2$?

Accepted Answer

$y = 5x + 7$

Question 13

If the graph of a line passes through $(0, -3)$ and $(6, 0)$, what is the equation of the line?

Accepted Answer

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

Question 14

Which of the following is the point-slope form of the equation of a line with slope $m$ passing through $(x_1, y_1)$?

Accepted Answer

$y - y_1 = m(x - x_1)$

Question 15

A line has equation $y = 4x + 1$. What is the slope of any line perpendicular to it?

Accepted Answer

$-\dfrac{1}{4}$

Question 16

Suppose you are given the equation $2x - 3y = 12$. What is the slope and $y$-intercept of the line?

Accepted Answer

Slope $= \dfrac{2}{3}$, $y$-intercept $= -4$

Question 17

Which of the following best describes the graph of a function with an undefined slope?

Accepted Answer

A vertical line

Question 18

If $f(x) = mx + b$ and $m = 0$, what kind of function is $f(x)$?

Accepted Answer

A constant function

Question 19

Given the line $y = -2x + 5$, what is the equation of the line passing through $(1, 3)$ and parallel to it?

Accepted Answer

$y = -2x + 5$

B1-B3

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