Question 1

Which of the following is the correct slope-intercept form of a line with a slope of $$\frac{2}{3}$$ and a y-intercept at $$(0, -1)$$?

Accepted Answer

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

Question 2

Given the line $$y = -3x - 2$$, what is the slope and y-intercept?

Accepted Answer

Slope: $$-3$$, y-intercept: $$-2$$

Question 3

Which equation represents a horizontal line passing through the point $$(4, 5)$$?

Accepted Answer

$$y = 5$$

Question 4

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

Accepted Answer

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

Question 5

Find the slope of the line passing through the points $$(1, 2)$$ and $$(4, 8).$$

Accepted Answer

$$2$$

Question 6

Which of the following is the equation of a line parallel to $$y = -\frac{1}{2}x + 3$$ and passing through $$(0, -4)$$?

Accepted Answer

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

Question 7

A company had 50 employees in 1997 and 85 employees in 2012. Assuming a linear relationship, what is the equation relating $$y ($$number of employees) to $$x ($$years after 1997)?

Accepted Answer

$$y = \frac{7}{3}x + 50$$

Question 8

Using the equation $$y = \frac{7}{3}x + 50$$, predict the number of employees in 2007.

Accepted Answer

$$y = 73$$

Question 9

Which of the following is the equation of a vertical line passing through $$(4, 5)$$?

Accepted Answer

$$x = 4$$

Question 10

What is the equation of the line perpendicular to $$y = 2x + 1$$ and passing through $$(2, 3)$$?

Accepted Answer

$$y - 3 = -\frac{1}{2}(x - 2)$$

Question 11

Given the line $$3x + 2y = 7$$, what is the slope of a line perpendicular to it?

Accepted Answer

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

Question 12

Which of the following is the standard form of the equation for a line passing through $$(1, 2)$$ with a slope of $$-3$$?

Accepted Answer

$$3x + y = 5$$

Question 13

If a line has an undefined slope and passes through $$(7, -2)$$, what is its equation?

Accepted Answer

$$x = 7$$

Question 14

Which of the following lines is perpendicular to $$y = \frac{1}{4}x - 2$$?

Accepted Answer

$$y = -4x + 1$$

Question 15

Given two points $$A(-4, 0)$$ and $$B(6, -1)$$, what is the slope of the line passing through them?

Accepted Answer

$$-\frac{1}{10}$$

Question 16

Which of the following is the correct equation in slope-intercept form for a line parallel to $$x + 3y = 6$$ and passing through $$(-2, 4)$$?

Accepted Answer

$$y = -\frac{1}{3}x + \frac{10}{3}$$

Question 17

A real estate agent uses the equation $$y = 150x + 20000 to $$estimate the value $$y of a $$house after $$x$$ years. What does the slope represent in this context?

Accepted Answer

The house increases in value by $150 each year.

Equations of Lines: Graphing, Forms, and Relationships

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