Question 558·Easy·Algebra

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x	y
0	−2
2	4
4	10
6	16

The table above lists several pairs of $x$ -values and their corresponding $y$ -values for a linear relationship. Which equation models this relationship?

A linear table gives you two pieces of slope-intercept form $y=mx+b$ : the slope $m$ and the intercept $b$ . Read the row where $x=0$ to find the intercept, then fit the table with Desmos’s Linear regression to find the slope. Don’t mistake an output change over several $x$ -units for the change per $1$ unit.

Hints

Hint 1
In $y=mx+b$ , $b$ is the $y$ -intercept: the output when the input is $0$ . Look at the row where $x=0$ . What value does it give for $b$ ?
Hint 2
The slope is the change in $y$ for each $1$ increase in $x$ . Fit a linear model to the table in Desmos. Which value does it report for $m$ ?

Step-by-step

Read the intercept and fit the line
Step 1
Find the intercept
The row $(0,-2)$ tells you that $y=-2$ when $x=0$ . The value of $y$ at $x=0$ is the $y$ -intercept, so $b=-2$ in $y=mx+b$ . An output from a row with a nonzero $x$ isn’t the intercept.
Step 2
Find the slope with Desmos
Enter the pairs in a Desmos table, with $x$ in $x_1$ and $y$ in $y_1$ . Then type $y_1\sim mx_1+b$ to fit a linear relationship. Desmos reports $m=3$ and $b=-2$ under PARAMETERS. The slope means $y$ rises $3$ for each $1$ increase in $x$ . For example, the rise from $-2$ to $4$ is $6$ , but it happens over $2$ units of $x$ , not $1$ .
Step 3
Write the matching equation
Put the slope and intercept into slope-intercept form $y=mx+b$ :
$y=3x-2.$
This models the table’s relationship. Choice D.

Question 558·Easy·Algebra

Strategy

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Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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