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?

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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