Question 1

A city is planning a new bike path that will pass through the points $$(-4, 1)$$ and $$(2, 4). $$What is the equation of the line in point-slope form that models the path?

Accepted Answer

Question 2

A line passes through the point $$(5, -4)$$ and has a slope of $$-\frac{1}{2}. $$What is its equation in point-slope form?

Accepted Answer

$$y + 4 = -\frac{1}{2}(x - 5)$$

Question 3

Which of the following is the slope-intercept form of the equation $$4x + 5y = 10$$?

Accepted Answer

$$y = -\frac{4}{5}x + 2$$

Question 4

A medical researcher plots the relationship between dosage and patient response. The line passes through $$(2, 3)$$ and $$(-1, 2). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = \frac{1}{3}x + \frac{7}{3}$$

Question 5

Given the equation $$x + 2y = -4$$, what are the slope and y-intercept?

Accepted Answer

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

Question 6

A business tracks its profit over time and finds the equation $$y = -2x + 1$$ fits the data. What does the slope represent in this context?

Accepted Answer

Profit decreases by $$2$$ units for each unit increase in time.

Question 7

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

Accepted Answer

$$y = -3x + 2$$

Question 8

A line passes through $$(3, 4)$$ and $$(1, 3). $$What is its equation in standard form $$Ax + By = C$$?

Accepted Answer

$$x - 2y = -1$$

Question 9

If a line has the equation $$y = 3x - 2$$, what is its x-intercept?

Accepted Answer

$$\frac{2}{3}$$

Question 10

A scientist records the temperature at different times and finds the equation $$y = -\frac{1}{2}x + 2$$ fits the data. What is the temperature when $$x = 4$$?

Accepted Answer

$$0$$

Question 11

Which of the following is the correct point-slope form for a line passing through $$(2, -3)$$ with slope $$4$$?

Accepted Answer

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

Question 12

A line has the equation $$y = -\frac{2}{5}x + 3. $$What is the slope and y-intercept?

Accepted Answer

Slope: $$-\frac{2}{5}$$, y-intercept: $$3$$

Question 13

Which equation represents a horizontal line passing through $$(0, 5)$$?

Accepted Answer

$$y = 5$$

Question 14

A line passes through $$(1, 3)$$ and $$(3, 7). $$What is its slope?

Accepted Answer

$$2$$

Question 15

Given the equation $$y = -3x + 11$$, what is the y-intercept?

Accepted Answer

$$11$$

Question 16

A line passes through $$(2, 5)$$ and has a slope of $$0. $$What is its equation?

Accepted Answer

$$y = 5$$

Question 17

Which of the following is the equation of a vertical line passing through $$x = -3$$?

Accepted Answer

$$x = -3$$

Question 18

A line passes through $$(0, 0)$$ and $$(4, 8). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 2x$$

Question 19

A line has the equation $$y = \frac{2}{3}x - 4. $$What is the value of $$y$$ when $$x = 6$$?

Accepted Answer

$$0$$

Question 20

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

Accepted Answer

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

Equations of Lines and Linear Models: Point-Slope and Slope-Intercept Forms

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