Question 1

Which of the following is the correct slope-intercept form for a line with a slope of $$\frac{3}{2}$$ and a y-intercept of $$-4$$?

Accepted Answer

$$y = \frac{3}{2}x - 4$$

Question 2

A line passes through the point $$(0, 5)$$ and has a slope of $$-2. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -2x + 5$$

Question 3

Which of the following equations represents a vertical line passing through $$x = -3$$?

Accepted Answer

$$x = -3$$

Question 4

Given the equation $$2x - 5y = 10$$, what is the slope and y-intercept when rewritten in slope-intercept form?

Accepted Answer

Question 5

A horizontal line passes through the point $$(0, 7). $$Which equation represents this line?

Accepted Answer

$$y = 7$$

Question 6

If a line has an undefined slope, which of the following statements is true?

Accepted Answer

The line is vertical.

Question 7

Given the general form $$Ax + By + C = 0$$, what is the x-intercept of the line?

Accepted Answer

$$x = -\frac{C}{A}$$

Question 8

A medical researcher plots the relationship between dosage (mg) and patient response (score) and finds the equation $$y = 1.5x + 2. $$What does the slope represent in this context?

Accepted Answer

The response score increases by 1.5 for each mg of dosage.

Question 9

Rewrite the equation $$3x + 4y = 12 in $$slope-intercept form.

Accepted Answer

$$y = -\frac{3}{4}x + 3$$

Question 10

A line passes through $$(2, 5)$$ and has a slope of $$-3. $$What is its equation in point-slope form?

Accepted Answer

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

Question 11

A chemical reaction is graphed as $$y = 0.5x + 1$$, where $$x is $$time in hours and $$y is $$concentration. What is the concentration after 4 hours?

Accepted Answer

$$y = 3$$

Question 12

Which of the following lines has a slope of zero?

Accepted Answer

$$y = 8$$

Question 13

If a line is given by $$y = -2x + 6$$, what is the y-intercept?

Accepted Answer

$$6$$

Question 14

A line passes through $$(0, -3)$$ and $$(2, 1). $$What is its slope?

Accepted Answer

$$2$$

Question 15

Given the equation $$x - 2y = 8$$, what are the x- and y-intercepts?

Accepted Answer

x-intercept: $$8$$, y-intercept: $$-4$$

Question 16

A historical event is modeled by $$y = 0.75x + 10$$, where $$x is $$years since 2000 and $$y is $$population in thousands. What is the population in 2025?

Accepted Answer

$$y = 28.75$$

Question 17

Which of the following is NOT a valid general form for a line?

Accepted Answer

$$0x + 0y + 5 = 0$$

Question 18

A line is given by $$y = 4x - 9. $$What is the slope and what does it mean in a real-world context where $$x is $$hours worked and $$y is $$dollars earned?

Accepted Answer

Slope: $$4. $$You earn $$4$$ dollars per hour.

Question 19

If a line is given in point-slope form as $$y - 2 = 5(x + 1)$$, what is its slope-intercept form?

Accepted Answer

$$y = 5x + 7$$

Graphing Linear Equations: Slope, Intercepts, and Forms

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