Q: Which of the following pairs of lines are parallel?

$$y = 3x + 1$$ \,\text{and}\, y = 3x - 4$

Question 1

Which of the following is the correct definition of a linear function?

Accepted Answer

$$f(x) = m 	imes x + b$$

Question 2

Given the linear function $$f(x) = 2x - 1$$, what are the slope and y-intercept?

Accepted Answer

Slope $$m = 2$$, y-intercept $$b = -1$$

Question 3

A company models its profit with the equation $$P(x) = 5x + 200$$, where $$x is $$the number of units sold. What does the slope represent in this context?

Accepted Answer

The profit per unit sold

Question 4

Given two points $$(3, 7)$$ and $$(5, 15) on a $$line, what is the slope of the line?

Accepted Answer

$$m = \frac{15 - 7}{5 - 3} = 4$$

Question 5

Which of the following equations represents a horizontal line passing through the point $$(1, 3)$$?

Accepted Answer

$$y = 3$$

Question 6

If a line has the equation $$y = -2x + 5$$, what is the y-intercept?

Accepted Answer

$$5$$

Question 7

Which of the following pairs of lines are parallel?

Accepted Answer

$$y = 3x + 1$$ \,	ext{and}\, y = 3x - 4$

Question 8

Find the equation of the line passing through $$(0, 3)$$ and $$(1, -1) in $$slope-intercept form.

Accepted Answer

$$y = -4x + 3$$

Question 9

A vertical line passes through the point $$(1, 3). $$What is its equation?

Accepted Answer

$$x = 1$$

Question 10

Which of the following is the correct point-slope form for a line with slope $$m = -5$$ passing through $$(-2, 7)$$?

Accepted Answer

$$y - 7 = -5(x + 2)$$

Question 11

If a line is perpendicular to the line $$y = \frac{1}{2}x + 3$$, what is its slope?

Accepted Answer

$$-2$$

Question 12

Given the table below, which value of $$f(x) is $$missing if the function is linear?

$$x$$: $$-2$$, $$0$$, $$1$$, $$2$$
$$f(x)$$: $$3$$, $$0$$, $$-3$$, $$?$$

Accepted Answer

$$-6$$

Question 13

A line contains the point $$(0, 3)$$ and is perpendicular to the line given by $$x + 2y = 7. $$What is the equation of the new line in slope-intercept form?

Accepted Answer

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

Question 14

Which of the following is NOT a possible application of linear equations?

Accepted Answer

Modeling exponential population growth

Question 15

Find the slope-intercept form of the line passing through $$(-1, 6)$$ and $$(2, 12).$$

Accepted Answer

Question 16

If the equation of a line is $$y = mx + b$$ and $$m = 0$$, what type of line is this?

Accepted Answer

Horizontal line

Question 17

Given the line $$y = 4x + 1$$, what is the equation of a line perpendicular to it passing through $$(0, 2)$$?

Accepted Answer

$$y = -\frac{1}{4}x + 2$$

Question 18

Which of the following statements is TRUE about the domain and range of a linear function $$f(x) = mx + b$$?

Accepted Answer

Domain is $$(-\infty, \infty)$$ and range is $$(-\infty, \infty)$$

Question 19

A line has the equation $$x = 6. $$What is the slope of this line?

Accepted Answer

Undefined

Question 20

Which of the following is the correct slope-intercept form for a line with slope $$m = 2$$ and y-intercept $$b = -4$$?

Accepted Answer

$$y = 2x - 4$$

Linear Functions and Equations of Lines: Precalculus Study Notes

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