Question 1

Is $$\left( -\frac{2}{3}, 8 \right) a $$solution to $$9x + y = 2$$?

Accepted Answer

No, because substituting $$x$$ and $$y$$ gives $$2.0.$$

Question 2

Find the $$x- $$and $$y-$$intercepts of $$-5x + 3y = -30.$$

Accepted Answer

$$x-$$intercept: $$(6, 0)$$; $$y-$$intercept: $$(0, 10)$$

Question 3

Which of the following best describes the graph of $$x = 4$$?

Accepted Answer

A vertical line passing through $$(4, 0)$$

Question 4

What is the slope of the line through $$(2, 1)$$ and $$(8, 4)$$?

Accepted Answer

$$\frac{1}{3}$$

Question 5

Find the slope of the line through $$(-3, -7)$$ and $$(-11, -11).$$

Accepted Answer

$$\frac{1}{2}$$

Question 6

In slope-intercept form, what is the equation of the line through $$(4, 6)$$ and $$(0, -2)$$?

Accepted Answer

$$y = 2x - 2$$

Question 7

Which of the following is the correct graph for the line through $$(1, 2)$$ with slope $$2$$?

Accepted Answer

A line passing through $$(1, 2)$$ and $$(2, 4)$$

Question 8

In slope-intercept form, what is the equation of the line with slope $$3$$ through the point $$(2, 5)$$?

Accepted Answer

$$y = 3x - 1$$

Question 9

In slope-intercept form, what is the equation of the line through the points $$(3, -6)$$ and $$(-6, 3)$$?

Accepted Answer

$$y = -x + 3$$

Question 10

What is the equation of a horizontal line through $$(2, -5)$$?

Accepted Answer

$$y = -5$$

Question 11

For the function $$g(x) = \frac{2x - 3}{x + 1}$$, find $$g(4).$$

Accepted Answer

$$1$$

Question 12

For the function $$g(x) = \frac{2x - 3}{x + 1}$$, find $$g(0).$$

Accepted Answer

$$-2$$

Question 13

For the function $$g(x) = \frac{2x - 3}{x + 1}$$, find $$g(-1).$$

Accepted Answer

Undefined

Question 14

Given the graph of $$f(x)$$, find all values of $$x$$ such that $$f(x) = -5.$$

Accepted Answer

$$x = -4$$ and $$x = 0$$

Question 15

For the function graphed below, state the domain and range in interval notation.

Accepted Answer

Domain: $$[-5, 5]$$; Range: $$[-3, 5]$$

Question 16

Which of the following is the correct graph for the piecewise function $$f(x) = \begin{cases} x & x \u003c 0 \ -x + 2 & x \geq 0 \end{cases}$$?

Accepted Answer

A line with slope $$1$$ for $$x \u003c 0$$ and a line with slope $$-1$$ for $$x \geq 0$$, both meeting at $$(0, 0)$$

Question 17

A biologist models the population of a bacteria culture with $$P(t) = 2t + 5$$ for $$t \geq 0. $$What is the population after $$3$$ hours?

Accepted Answer

$$11$$

Question 18

A car rental company charges a flat fee of $$\20$ plus $$\$$0.50$$ per mile driven. Which equation models the total cost $$C$$ for $$m$$ miles?

Accepted Answer

$$C = 0.5m + 20$$

Question 19

A medication's concentration in the bloodstream is modeled by $$C(t) = -2t + 10$$ for $$t \geq 0. $$After how many hours will the concentration reach $$0$$?

Accepted Answer

$$5$$ hours

Question 20

A line passes through $$(0, 3)$$ and has a slope of $$-4. $$What is its equation in slope-intercept form?

Accepted Answer

$$y = -4x + 3$$

Intermediate Algebra Study Guide: Linear Equations, Functions, and Graphs

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