Question 589·Medium·Math

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The linear function $g$ is represented by the table below.

$x$	$g(x)$
-1	4
1	0
3	-4

Which equation defines $g(x)$ ?

A table of input-output pairs for a linear function describes one straight-line rule. Plot the pairs in Desmos, then fit a line to find its slope and its output when the input is $0$ . Match both parts of the rule. An output of $0$ in the table does not necessarily give the output at input $0$ .

Hints

Hint 1
Each table row is a point: the first column is the input, and the second is the output. As the inputs increase, do the outputs rise or fall? That tells you the sign of the slope, the change in output per input step.
Hint 2
A line in slope-intercept form uses $m$ for its slope and $b$ for its output when the input is $0$ . Fit the table pairs in Desmos to find both numbers, rather than relying on one row.
Hint 3
The row with an output of $0$ gives an $x$ -intercept, where the line crosses the horizontal axis. To find the $y$ -intercept, you need an input of zero. Does the table have that row?

Step-by-step

Fit a line to the table
Step 1
Plot the table pairs
Enter the table in Desmos with the inputs under $x_1$ and their matching outputs under $y_1$ . The plotted points fall from left to right. So the slope, the output change for each increase of $1$ in the input, must be negative.
Step 2
Read the slope and intercept
On a new line, type $y_1\sim mx_1+b$ . The $\sim$ asks Desmos to fit a line to the table. Under PARAMETERS, it shows $m=-2$ and $b=2$ . Here $b$ is the $y$ -intercept, the output when the input is $0$ . The table’s output of $0$ occurs at input $1$ , so it is not the $y$ -intercept.
Step 3
Write the rule
Put those values into slope-intercept form, $g(x)=mx+b$ :
$g(x)=-2x+2.$
That gives the table’s decreasing line. Choice B.

Question 589·Medium·Math

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Hints

Step-by-step

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