Question 1

Rewrite the equation $$x - y = 5 in $$slope-intercept form. What is the x-intercept of the function?

Accepted Answer

Slope-intercept form: $$y = x - 5$$; x-intercept: $$(5, 0)$$

Question 2

Which equation represents a line with slope $$-\frac{3}{4}$$ and y-intercept $$2$$?

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Given the equation $$6x + 3y = 18$$, what is the slope of the line?

Accepted Answer

Slope: $$-2$$

Question 5

What is the y-intercept of the line $$6x + 3y = 18$$?

Accepted Answer

y-intercept: $$(0, 6)$$

Question 6

What is the x-intercept of the line $$6x + 3y = 18$$?

Accepted Answer

x-intercept: $$(6, 0)$$

Question 7

Which equation is parallel to $$2x + y = 7$$ and passes through $$(-1, 4)$$?

Accepted Answer

$$y = 2x + 6$$

Question 8

A real estate agent models the price of a house as a linear function of its size. If a $$1000 sq ft $$house costs $$\150$$,000$$ and a 2000$ sq ft house costs $$\$$250,000$$, what is the equation for price $$P in $$terms of size $$S$$?

Accepted Answer

$$P = 100S + 50,000$$

Question 9

If the equation of a line is $$y = -2x + 2$$, what is the slope and y-intercept?

Accepted Answer

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

Question 10

Which equation represents a line perpendicular to $$y = 2x + 6$$ and passes through $$(0, 6)$$?

Accepted Answer

$$y = -\frac{1}{2}x + 6$$

Question 11

A chemist mixes two solutions. The concentration $$C (in mg/L) $$increases linearly with time $$t (in $$hours). If $$C = 10 at$$ $$t = 2$$ and $$C = 22 at$$ $$t = 5$$, what is the equation for $$C in $$terms of $$t$$?

Accepted Answer

$$C = 4t + 2$$

Question 12

A medical researcher finds that the number of bacteria $$N in a $$culture grows linearly with time $$t. If$$ $$N = 500 at$$ $$t = 1$$ hour and $$N = 1100 at$$ $$t = 4$$ hours, what is the equation for $$N in $$terms of $$t$$?

Accepted Answer

$$N = 200t + 300$$

Question 13

A line has equation $$y = -(3/4)x + 2. $$What is the x-intercept?

Accepted Answer

x-intercept: $$(\frac{8}{3}, 0)$$

Question 14

Which equation is parallel to $$y = -2x + 6$$ and passes through $$(1, 4)$$?

Accepted Answer

Question 15

A car rental company charges a flat fee of $$\30$ plus $$\$$0.20$$ per mile driven. Write the equation for the total cost $$C in $$terms of miles $$m.$$

Accepted Answer

$$C = 0.20m + 30$$

Question 16

A line passes through $$(2, -1)$$ and $$(4, 3). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 2x - 5$$

Question 17

A biologist records the height $$h (in cm) of a $$plant as a linear function of days $$d. If$$ $$h = 15 at$$ $$d = 3$$ and $$h = 27 at$$ $$d = 7$$, what is the equation for $$h in $$terms of $$d$$?

Accepted Answer

$$h = 3d + 6$$

Question 18

Which equation represents a line with slope $$\frac{1}{2}$$ and y-intercept $$\frac{9}{2}$$?

Accepted Answer

$$y = \frac{1}{2}x + \frac{9}{2}$$

Question 19

A line passes through $$(0, 5)$$ and $$(2, 9). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = 2x + 5$$

College Algebra: Linear Equations, Slope, and Intercepts Study Guide

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