Question 633·Easy·Math

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The values of the linear function $f$ are shown in the table.

$x$	$f(x)$
0	29
1	32
2	35

Which equation defines $f(x)$ ?

A table of a linear function gives you two facts to look for: the output at input $0$ and how much the output changes per input step. Use those as the intercept and slope in $f(x)=mx+b$ . A Desmos table regression can check both values. Compare rows to find the slope; don’t mistake a table output for it.

Hints

Hint 1
The $y$ -intercept is the output when $x=0$ , because the $mx$ part of $f(x)=mx+b$ becomes $0$ . Which row has input $0$ , and what does its output tell you about $b$ ?
Hint 2
The slope is the change in output for each increase of $1$ in input. Compare two neighboring rows, then check the next pair of rows for the same change. What number should multiply $x$ ?

Step-by-step

Find the intercept and slope from the table
Step 1
Read the output at zero
The row where $x=0$ says $f(0)=29$ . In $f(x)=mx+b$ , $b$ is the $y$ -intercept, or output at input $0$ , because $m(0)=0$ . So $b=29$ .
Step 2
Find the slope with Desmos
Enter the three table rows in Desmos, then type $y_1\sim mx_1+b$ . The symbols $x_1$ and $y_1$ name the table columns; $\sim$ tells Desmos to fit the line. Under PARAMETERS, it reports $m=3$ and $b=29$ . The slope $m$ means the output rises by $3$ whenever the input rises by $1$ , as it does from $29$ to $32$ to $35$ .
Step 3
Write the function
Use slope-intercept form $f(x)=mx+b$ : the slope multiplies $x$ , and the intercept is added. With $m=3$ and $b=29$ , the function is $f(x)=3x+29$ . Choice D.

Question 633·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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