Question 212·Easy·Algebra

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

For line questions asking for the $y$ -intercept, quickly put the line into slope-intercept form $y = mx + b$ . Use the given slope for $m$ , plug in the coordinates of any point on the line for $x$ and $y$ , and solve the simple one-step equation to find $b$ . This avoids unnecessary graphing and gets you to the answer efficiently.

Hints

Click me!

Recall the form of a line

Think about the slope-intercept form of a line, which shows the slope and the $y$ -intercept directly.

Use the given slope and point

Write the line as $y = 3x + b$ , then plug in $x=2$ and $y=5$ because the point $(2,5)$ is on the line.

Solve for the unknown

After substituting, isolate $b$ by performing the same operation on both sides of the equation.

Desmos Guide

Enter the line using point-slope form

Type the equation $y - 5 = 3(x - 2)$ into Desmos. This represents a line with slope $3$ passing through $(2,5)$ .

Find the y-intercept from the graph

Look at where the line crosses the $y$ -axis (where $x=0$ ). Click that intersection point; the $y$ -coordinate of this point is the $y$ -intercept you want.

Step-by-step Explanation

Write the slope-intercept form

A line with slope $m$ and $y$ -intercept $b$ can be written as

y = mx + b

Here, the slope is $3$ , so the equation becomes

y = 3x + b.

Substitute the given point into the equation

The line passes through $(2,5)$ , so $x=2$ and $y=5$ must satisfy the equation.

Substitute $x=2$ and $y=5$ into $y = 3x + b$ :

5 = 3(2) + b.

Solve for b, the y-intercept

Now solve for $b$ :

5 = 6 + b \\[0.7em] 5 - 6 = b \\[0.7em] -1 = b.

So the $y$ -intercept of the line is $-1$ , which corresponds to choice B.

Question 212·Easy·Algebra

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation