Question 729·Easy·Math

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A line has slope $3$ and passes through the point $(2,5)$ . What is the $y$ -intercept of the line?

A y-intercept is the line’s $y$ -value where $x=0$ . If you know a slope and a point with a nonzero $x$ -coordinate, use $y=mx+b$ and substitute the point to find $b$ . Desmos can solve the resulting equation for that missing constant. Don’t mistake the point’s $y$ -value for the intercept.

Hints

Hint 1
In slope-intercept form, $y=mx+b$ , the number $m$ is the slope and $b$ is the value of $y$ when $x=0$ . The slope is given; what does that make the equation?
Hint 2
The point $(2,5)$ means $y=5$ when $x=2$ , not when $x=0$ . Put both coordinates into your equation. What must the unknown y-intercept $b$ satisfy?

Step-by-step

Use the slope and point
Step 1
Write the line with an unknown intercept
Use slope-intercept form $y=mx+b$ , where $m$ is the slope and $b$ is the $y$ -value when $x=0$ . Put the given slope of $3$ in for $m$ :
$y=3x+b.$
Step 2
Put the point into the equation
The point $(2,5)$ means $x=2$ gives $y=5$ . Substitute both coordinates:
$5=3(2)+b.$
The $5$ isn’t the y-intercept: it occurs at $x=2$ , not $x=0$ .
Step 3
Solve for the intercept
In Desmos, type $5\sim3(2)+b$ . The $\sim$ tells Desmos to find the missing constant. Under PARAMETERS, it shows $b=-1$ . So the line crosses the $y$ -axis at $(0,-1)$ , and the requested $y$ -intercept is $-1$ . Choice B.

Question 729·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

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Strategy

Hints

Step-by-step

Lessons that teach this