Question 322·Medium·Algebra

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A line passes through the points $(-4,3)$ and $(8,-9)$ . Which of the following is the equation of the line in slope-intercept form?

Two points determine a line, but slope-intercept form $y=mx+b$ needs both the slope $m$ and the intercept $b$ . Find the slope by dividing the change in $y$ by the matching change in $x$ , then put either point into the equation to find $b$ . Desmos can handle the arithmetic and solve for the unknown. A point's $y$ -value is the intercept only when its $x$ -value is $0$ .

Hints

Hint 1
The slope compares how much $y$ changes with how much $x$ changes. Subtract the coordinates in the same order on top and bottom: if you start with the second point's $y$ , start with its $x$ too.
Hint 2
In $y=mx+b$ , the intercept $b$ is the value of $y$ when $x=0$ . Neither given point has $x=0$ , so use one point and the slope to find what $b$ must be.

Step-by-step

Find the slope, then the intercept
Step 1
Find the slope from the two points
The slope $m$ is the change in $y$ divided by the change in $x$ . Subtract the points in the same order on top and bottom. Type $\frac{-9-3}{8-(-4)}$ in Desmos; it shows $-1$ . So $y$ falls by $1$ each time $x$ rises by $1$ .
Step 2
Turn one point into an intercept equation
In slope-intercept form $y=mx+b$ , $b$ is the value of $y$ when $x=0$ . The point $(-4,3)$ says $y=3$ when $x=-4$ , so substitute it and the slope $-1$ :
$3=-1(-4)+b$
Don't use $3$ as the intercept: this point's $x$ -value isn't $0$ .
Step 3
Solve for the intercept and name the line
Keep the slope calculation and type $3\sim-1(-4)+b$ . The $\sim$ tells Desmos to solve for the unknown intercept; under PARAMETERS, it shows $b=-1$ . So the line's equation is $y=-x-1$ . Choice D.

Question 322·Medium·Algebra

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

Lessons that teach this