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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