Learn on PengiBig Ideas Math, Course 2, AcceleratedChapter 3: Graphing and Writing Linear Equations

Lesson 7: Writing Equations in Point-Slope Form

Property The point slope form of a linear equation is $y = y 1 + m(x x 1)$, where $m$ is the slope and $(x 1, y 1)$ is any known point on the line.

Section 1

Point-Slope Form

Property

The point-slope form of a linear equation is y=y1+m(x−x1)y = y_1 + m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is any known point on the line.

This form is useful for finding the equation of a line when you know its slope and at least one point it passes through.

You may also see the formula written in an alternate version:

y−y1=m(x−x1)ory−y1x−x1=my-y_1=m(x-x_1) \quad \text{or} \quad \frac{y-y_1}{x-x_1}=m

Section 2

Writing Equations Using Two Points

Property

When given two points, first find the slope using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. Then, choose one of the points and use the point-slope form, y−y1=m(x−x1)y - y_1 = m(x - x_1), to write the equation of the line.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Point-Slope Form

Property

The point-slope form of a linear equation is y=y1+m(x−x1)y = y_1 + m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is any known point on the line.

This form is useful for finding the equation of a line when you know its slope and at least one point it passes through.

You may also see the formula written in an alternate version:

y−y1=m(x−x1)ory−y1x−x1=my-y_1=m(x-x_1) \quad \text{or} \quad \frac{y-y_1}{x-x_1}=m

Section 2

Writing Equations Using Two Points

Property

When given two points, first find the slope using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. Then, choose one of the points and use the point-slope form, y−y1=m(x−x1)y - y_1 = m(x - x_1), to write the equation of the line.

Examples