Question 578·Medium·Algebra

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The table lists several pairs $(x,y)$ that lie on the same line. Which equation could represent the relationship between $x$ and $y$ ?

$x$	$y$
1	17
4	11
10	-1

A table of points on one line points to slope-intercept form, $y=mx+b$ : $m$ is the change in $y$ for each $1$ added to $x$ , and $b$ is the value when $x=0$ . Enter the pairs in a Desmos table and fit that form to find both numbers. The first output listed is not necessarily the intercept; check its input.

Hints

Hint 1
Each table row is a point: the first column is the input, and the second is its output. Plot the rows in a Desmos table. As the inputs increase, do the outputs rise or fall? That tells you the sign of the slope.
Hint 2
Use slope-intercept form $y=mx+b$ . Fit $y_1\sim mx_1+b$ to the table; the tilde asks Desmos to find $m$ and $b$ . Which number tells you how fast $y$ changes?
Hint 3
The $y$ -intercept is the output when $x=0$ , not the first output listed. Read $m$ and $b$ under PARAMETERS, then put both numbers into $y=mx+b$ .

Step-by-step

Fit a line to the table
Step 1
Plot the table's points
Each row gives a point $(x,y)$ on the line. Enter the three rows in a Desmos table with columns $x_1$ and $y_1$ . Desmos plots $(1,17)$ , $(4,11)$ , and $(10,-1)$ . The dots fall as $x$ grows, so the slope, or change in $y$ per $1$ added to $x$ , must be negative.
Step 2
Find the slope and intercept
Type $y_1\sim mx_1+b$ . The tilde tells Desmos to find the numbers that fit the table to $y=mx+b$ . Under PARAMETERS, Desmos shows $m=-2$ and $b=19$ . Here $m$ is the slope, and the $y$ -intercept $b$ is the output when $x=0$ . The table's $17$ is not $b$ : it belongs to $x=1$ .
Step 3
Write the equation
Put the fitted slope and intercept into $y=mx+b$ :
$y=-2x+19.$
This equation represents the line through the table's points. Choice A.

Question 578·Medium·Algebra

Strategy

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Step-by-step

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Strategy

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