Linear functions from tables Practice Questions (Grade 9)

Warm-upeasy

Taxi cost, in dollars, after $x$ miles:
$\begin{array}{c|c} x & f(x) \\ \hline 1 & 6 \\ 2 & 10 \\ 3 & 14 \\ 4 & 18 \end{array}$
The cost is $f(x)=mx+2\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The cost increases by $\text{\char36}4$ per mile, so $m = 4\textsf{.}$

Mid-gameeasy

Tutoring cost, in dollars, for $x$ lessons:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline f(x) & 40 & 65 & 90 & 115 \end{array}$
The cost is $f(x)=25x+b\textsf{.}$ What is $b\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ When $x = 0$ , the cost is $f(0) = 40$ , so $b = 40\textsf{.}$

Mid-gameeasy

Tree height, in feet, after $x$ years:
$\begin{array}{c|c} x & f(x) \\ \hline 1 & 20 \\ 2 & 28 \\ 3 & 36 \\ 4 & 44 \end{array}$
The height is $f(x)=mx+12\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The height increases by $8$ feet each year, so $m = 8\textsf{.}$

Mid-gameeasy

Water left, in gallons, after $x$ hours:
$\begin{array}{c|c} x & f(x) \\ \hline 0 & 48 \\ 1 & 42 \\ 2 & 36 \\ 3 & 30 \end{array}$
The amount is $f(x)=-6x+b\textsf{.}$ What is $b\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ When $x = 0\textsf{,}$ the amount remaining is $f(0) = 48\textsf{,}$ so $b = 48\textsf{.}$

Mid-gameeasy

Bike rental cost, in dollars, for $x$ hours:
$\begin{array}{c|cccc} x & 0 & 1 & 2 & 3 \\ \hline f(x) & 10 & 16 & 22 & 28 \end{array}$
The cost is $f(x)=6x+b\textsf{.}$ What is $b\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ When $x = 0\textsf{,}$ the cost is $f(0) = 10\textsf{,}$ so $b = 10\textsf{.}$

Mid-gamemedium

Candle height, in cm, after $x$ hours:
$\begin{array}{c|c} x & f(x) \\ \hline 0 & 20 \\ 1 & 18 \\ 2 & 16 \\ 3 & 14 \end{array}$
The height is $f(x)=mx+20\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The height decreases by $2$ centimeters each hour, so $m = -2\textsf{.}$

Mid-gamemedium

Phone charge, in dollars, for $x$ extra minutes:
$\begin{array}{c|cccc} x & 0 & 5 & 10 & 15 \\ \hline f(x) & 30 & 40 & 50 & 60 \end{array}$
The charge is $f(x)=mx+30\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The charge increases by $\text{\char36}2$ for each extra minute, so $m = 2\textsf{.}$

Buzzer beatermedium

Temperature, in $^\circ$ F, after $x$ hours past noon:
$\begin{array}{c|c} x & f(x) \\ \hline 2 & 62 \\ 4 & 56 \\ 6 & 50 \\ 8 & 44 \end{array}$
The temperature is $f(x)=mx+68\textsf{.}$ What is $m\textsf{?}$

Slope-intercept form is $f(x) = mx + b\textsf{.}$ The temperature decreases by $3$ degrees each hour, so $m = -3\textsf{.}$

Linear functions from tables (ACT/SAT). Game on.

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