Question 1050·Easy·Math

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What is the equation of the line that passes through the points $(2,3)$ and $(4,7)$ in the $xy$ -plane?

Two points with different $x$ -values determine one line. Find its slope by dividing the change in $y$ by the change in $x$ , keeping the subtraction order the same. Then put either point into $y=mx+b$ to find $b$ , the value of $y$ when $x=0$ . A point’s $y$ -value isn’t automatically the intercept.

Hints

Hint 1
The slope compares how much $y$ changes with how much $x$ changes. Keep the subtractions in the same order: from the first point to the second, what are the two changes?
Hint 2
In slope-intercept form, $y=mx+b$ , the number $b$ is the value of $y$ when $x=0$ . Neither given point has $x=0$ , so put a point into the equation to find $b$ .

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 $x$ . From $(2,3)$ to $(4,7)$ , type $\frac{7-3}{4-2}$ in Desmos. It displays $2$ , so $m=2$ . Keep the points in the same subtraction order on top and bottom.
Step 2
Use one point to find the intercept
In slope-intercept form $y=mx+b$ , $b$ is the value of $y$ at $x=0$ . The point $(2,3)$ says $y=3$ at $x=2$ , not at $x=0$ . With $m=2$ , it gives $3=2(2)+b$ . Type $3\sim2(2)+b$ in Desmos; $\sim$ asks it to find $b$ . Under PARAMETERS, Desmos shows $b=-1$ .
Step 3
Write the line’s equation
Use both facts. Substitute $m=2$ and $b=-1$ into $y=mx+b$ :
$y=2x-1.$
That’s the equation of the line through the two given points. Choice D.

Question 1050·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this