Question 1

Which of the following is the correct definition of the slope $$m of a $$nonvertical line passing through two distinct points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \dfrac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 2

Given the points $$A(-3, 4)$$ and $$B(2, -1)$$, what is the slope of the line passing through them?

Accepted Answer

Question 3

Which of the following lines has an undefined slope?

Accepted Answer

$$x = -2$$

Question 4

What is the equation of the line in point-slope form that passes through the point $$(2, -3)$$ with slope $$m = 4$$?

Accepted Answer

$$y + 3 = 4(x - 2)$$

Question 5

Convert the point-slope equation $$y + 2 = -3(x - 1) to $$slope-intercept form.

Accepted Answer

Question 6

Which of the following is the standard form of a linear equation?

Accepted Answer

$$Ax + By = C$$

Question 7

A horizontal line passes through the point $$(0, -7). $$What is its equation?

Accepted Answer

$$y = -7$$

Question 8

If a line has a slope of $$0$$, which of the following statements is true?

Accepted Answer

The line is horizontal.

Question 9

Find the $$y-$$intercept of the line given by $$2x - 3y = 6.$$

Accepted Answer

$$(0, -2)$$

Question 10

A real-world scenario: A taxi company charges a flat fee of $$\3$ plus $$\$$2$$ per mile. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 2m + 3$$

Question 11

Which of the following equations represents a vertical line passing through $$(4, -2)$$?

Accepted Answer

$$x = 4$$

Question 12

Given the equation $$y = -\dfrac{1}{2}x + 5$$, what is the slope and $$y-$$intercept?

Accepted Answer

Slope: $$-\dfrac{1}{2}$$, $$y-$$intercept: $$5$$

Question 13

A line passes through $$(1, 2)$$ and $$(5, 10). $$What is its equation in slope-intercept form?

Accepted Answer

Question 14

Which of the following is NOT a linear equation?

Accepted Answer

$$y = x^2$ + 3$$

Question 15

If a line passes through $$(0, 5)$$ and has a slope of $$-3$$, what is its equation in slope-intercept form?

Accepted Answer

$$y = -3x + 5$$

Question 16

A biologist records the height $$h (in cm) of a $$plant as a function of time $$t (in $$weeks) using the equation $$h = 2t + 10. $$What does the $$10$$ represent in this context?

Accepted Answer

The initial height of the plant at $$t = 0$$

Question 17

Which of the following statements is true about the line $$y = 7$$?

Accepted Answer

It is a horizontal line with slope $$0$$

Question 18

Find the $$x-$$intercept of the line $$3x + 6y = 12.$$

Accepted Answer

$$(4, 0)$$

Question 19

A line passes through $$(2, 5)$$ and is parallel to the line $$y = -3x + 1. $$What is its equation in point-slope form?

Accepted Answer

$$y - 5 = -3(x - 2)$$

Study Notes: Lines and Their Equations (Section 2.3)

Study Guide - Practice Questions

Study Guide - Flashcards