Question 1

Given the equation of a line in point-slope form $$y - y_1$ = m(x - x_1$)$$, which of the following represents the equation of a line passing through the point $$(3, -2)$$ with a slope of $$4$$?

Accepted Answer

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

Question 2

Which of the following is the slope-intercept form of the equation $$y + 2 = 4(x - 3)$$?

Accepted Answer

$$y = 4x - 14$$

Question 3

If a line passes through the points $$(1, 2)$$ and $$(3, 6)$$, what is its slope?

Accepted Answer

$$2$$

Question 4

Which of the following points lies on the line $$y = 2x - 5$$?

Accepted Answer

$$(3, 1)$$

Question 5

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.

Question 6

Which equation represents a line parallel to $$y = -3x + 7$$ and passing through $$(0, -2)$$?

Accepted Answer

$$y = -3x - 2$$

Question 7

If the equation of a line is $$2x - 3y = 6$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, -2)$$

Question 8

A biologist tracks the growth of a bacteria population with the equation $$P = 500 + 20t$$, where $$P is $$the population after $$t$$ hours. What is the initial population?

Accepted Answer

$$500$$

Question 9

Which of the following lines is perpendicular to $$y = \frac{1}{2}x + 3$$?

Accepted Answer

$$y = -2x + 1$$

Question 10

A car rental company charges a flat fee of $$\25$ plus $$\$$0.15$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 0.15m + 25$$

Question 11

If a line has the equation $$y = -\frac{2}{3}x + 4$$, what is the slope?

Accepted Answer

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

Question 12

Which of the following is the equation of a line with an undefined slope passing through $$(5, -3)$$?

Accepted Answer

$$x = 5$$

Question 13

A chemist cools a solution from $$80^\circC at a $$rate of $$5^\circC $$per minute. Which equation models the temperature $$T$$ after $$t$$ minutes?

Accepted Answer

$$T = 80 - 5t$$

Question 14

Which of the following is the equation of a line passing through $$(2, 5)$$ and $$(4, 9)$$?

Accepted Answer

$$y = 2x + 1$$

Question 15

If the equation of a line is $$y = mx + b$$ and the line passes through $$(0, 7)$$, what is the value of $$b$$?

Accepted Answer

$$7$$

Graphing Linear Equations and Finding the Equation of a Line

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