Question 453·Easy·Algebra

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Line $\ell$ passes through the points $(4,-2)$ and $(8,6)$ . Which equation represents line $\ell$ ?

Two points with different $x$ -values determine one linear equation. Enter the points in a Desmos table and fit a line to find its slope, the change in $y$ for each $1$ in $x$ , and its $y$ -intercept, the value when $x=0$ . Match both the slope and the intercept; the right slope alone can still give the wrong line.

Hints

Hint 1
The slope tells you how much $y$ changes when $x$ increases by $1$ . Because the two points have different inputs, Desmos can fit a line through them. What value does it report for the slope?
Hint 2
In $y=mx+b$ , $b$ is the y-intercept: the value of $y$ when $x=0$ . Neither given point has $x=0$ , so its $y$ -value isn't automatically $b$ . What sign does Desmos show for $b$ ?

Step-by-step

Fit a line through the two points
Step 1
Find the slope and intercept in Desmos
Each point is an $(x,y)$ pair, so enter $4,8$ in the table's $x_1$ column and $-2,6$ in its $y_1$ column. Then type $y_1\sim mx_1+b$ ; the tilde tells Desmos to fit a line through the points. Here $m$ is the slope, and $b$ is the y-intercept, the value when $x=0$ . Under PARAMETERS, Desmos shows $m=2$ and $b=-10$ .
Step 2
Write the equation of the line
Put those values into slope-intercept form, $y=mx+b$ : $y=2x-10$ . Keep the minus sign on the intercept. Line $\ell$ is $y=2x-10$ . Choice D.

Question 453·Easy·Algebra

Strategy

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Step-by-step

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Strategy

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Step-by-step

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