Q: Which of the following is always true for a linear function $$f(x) = mx + b$$?

It has exactly one zero if $$m \neq 0.$$

Question 1

Which of the following best describes a linear equation in one variable?

Accepted Answer

An equation that can be written in the form $$ax + b = 0$$, where $$a$$ and $$b$$ are real numbers and $$a 
eq 0.$$

Question 2

What is the solution to the equation $$\frac{2}{3}x - \frac{1}{5} = \frac{7}{5}$$?

Accepted Answer

$$x = 6$$

Question 3

Which principle allows you to add the same value to both sides of an equation without changing the solution?

Accepted Answer

The Addition Principle

Question 4

Solve for $$x$$: $$3 - \frac{1}{3}x = \frac{1}{3}x + 3$$

Accepted Answer

$$x = 0$$

Question 5

If the equation $$-24x + 7 = 17 - 24x is $$solved, what is the solution?

Accepted Answer

All real numbers

Question 6

The distance $$d$$ traveled by an object moving at rate $$r in $$time $$t is $$given by $$d = rt. If a $$car travels at $$60$$ mph for $$2.5$$ hours, how far does it travel?

Accepted Answer

$$150$$ miles

Question 7

A student loan accrues $$5\%$$ simple interest annually. If the loan amount is $$\5000$, how much interest is owed after 3$ years?

Accepted Answer

$$\750$

Question 8

Which of the following is the zero of the function $$f(x) = 2x - 12$$?

Accepted Answer

$$x = 6$$

Question 9

A salesperson earns a base salary of $$\1200$ plus 8$$\%$$ commission on sales. If the salesperson earned $$\$$1712 in a $$month, what were their total sales?

Accepted Answer

$$\6400$

Question 10

The width of a rectangular field is $$12 ft $$less than its length. If the perimeter is $$144 ft$$, what is the length of the field?

Accepted Answer

$$33 ft$$

Question 11

Which of the following is always true for a linear function $$f(x) = mx + b$$?

Accepted Answer

It has exactly one zero if $$m 
eq 0.$$

Question 12

If $$f(x) = 4x - 8$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 2$$

Question 13

Which equation represents a line with slope $$m = -3$$ and $$y-$$intercept $$b = 5$$?

Accepted Answer

$$y = -3x + 5$$

Question 14

If $$3x - 5 = 2x + 7$$, what is the value of $$x$$?

Accepted Answer

$$x = 12$$

Question 15

A train travels $$d$$ miles at a constant speed $$r in$$ $$t$$ hours. If $$d = 240$$ miles and $$t = 3$$ hours, what is the speed?

Accepted Answer

$$80$$ mph

Linear Equations and Zeros of Linear Functions

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