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

$$y = -2x + 5$$

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