Learn on PengiCalifornia Reveal Math, Algebra 1Unit 4: Creating Linear Equations

4-2 Writing Equations in Standard and Point-Slope Forms

In this Grade 9 Algebra 1 lesson from California Reveal Math, students learn to write linear equations in point-slope form using the formula y minus y₁ equals m times x minus x₁, given a slope and a point or two points on a line. Students also practice converting between point-slope form, slope-intercept form, and standard form, including applying these skills to real-world contexts. The lesson is part of Unit 4: Creating Linear Equations and builds fluency in translating among equivalent representations of linear equations.

Section 1

Point-Slope Form: Definition and Structure

Property

The point-slope form of a linear equation is:

y - y_1 = m(x - x_1)

Section 2

Writing Equations Using Slope and One Point

Property

To find an equation of a line with a given slope and a point, substitute the slope and the coordinates of the point into the point-slope form: $y - y_1 = m(x - x_1)$ .

Examples

Section 3

Converting Point-Slope to Slope-Intercept Form

Property

To convert from point-slope form to slope-intercept form, solve for $y$ :

y - y_1 = m(x - x_1) \rightarrow y = mx - mx_1 + y_1

Examples

Section 4

Converting Point-Slope to Standard Form

Property

To convert from point-slope form $y - y_1 = m(x - x_1)$ to standard form $Ax + By = C$ :

Distribute the slope on the right side
Move all terms with variables to the left side
Ensure $A > 0$ and $A$ , $B$ , $C$ have no common factors

Examples

Book overview

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Continue this chapter

Unit 4: Creating Linear Equations

Back to California Reveal Math, Algebra 1

Lesson 1
4-1 Writing Equations in Slope-Intercept Form
Learn Practice
Lesson 2Current
4-2 Writing Equations in Standard and Point-Slope Forms
Learn Practice
Lesson 3
4-3 Scatter Plots and Lines of Fit
Learn Practice
Lesson 4
4-4 Linear Regression
Learn Practice
Lesson 5
4-5 Inverses of Linear Functions
Learn Practice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Point-Slope Form: Definition and Structure

Property

The point-slope form of a linear equation is:

y - y_1 = m(x - x_1)

Section 2

Writing Equations Using Slope and One Point

Property

To find an equation of a line with a given slope and a point, substitute the slope and the coordinates of the point into the point-slope form: $y - y_1 = m(x - x_1)$ .

Examples

Section 3

Converting Point-Slope to Slope-Intercept Form

Property

To convert from point-slope form to slope-intercept form, solve for $y$ :

y - y_1 = m(x - x_1) \rightarrow y = mx - mx_1 + y_1

Examples

Section 4

Converting Point-Slope to Standard Form

Property

To convert from point-slope form $y - y_1 = m(x - x_1)$ to standard form $Ax + By = C$ :

Distribute the slope on the right side
Move all terms with variables to the left side
Ensure $A > 0$ and $A$ , $B$ , $C$ have no common factors

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Unit 4: Creating Linear Equations

Back to California Reveal Math, Algebra 1

Lesson 1
4-1 Writing Equations in Slope-Intercept Form
Learn Practice
Lesson 2Current
4-2 Writing Equations in Standard and Point-Slope Forms
Learn Practice
Lesson 3
4-3 Scatter Plots and Lines of Fit
Learn Practice
Lesson 4
4-4 Linear Regression
Learn Practice
Lesson 5
4-5 Inverses of Linear Functions
Learn Practice

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Point-Slope Form: Definition and Structure

Property

The point-slope form of a linear equation is:

y - y_1 = m(x - x_1)

Section 2

Writing Equations Using Slope and One Point

Property

To find an equation of a line with a given slope and a point, substitute the slope and the coordinates of the point into the point-slope form: $y - y_1 = m(x - x_1)$ .

Examples

Section 3

Converting Point-Slope to Slope-Intercept Form

Property

To convert from point-slope form to slope-intercept form, solve for $y$ :

y - y_1 = m(x - x_1) \rightarrow y = mx - mx_1 + y_1

Examples

Section 4

Converting Point-Slope to Standard Form

Property

To convert from point-slope form $y - y_1 = m(x - x_1)$ to standard form $Ax + By = C$ :

Distribute the slope on the right side
Move all terms with variables to the left side
Ensure $A > 0$ and $A$ , $B$ , $C$ have no common factors

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Unit 4: Creating Linear Equations

Back to California Reveal Math, Algebra 1

Lesson 1
4-1 Writing Equations in Slope-Intercept Form
Learn Practice
Lesson 2Current
4-2 Writing Equations in Standard and Point-Slope Forms
Learn Practice
Lesson 3
4-3 Scatter Plots and Lines of Fit
Learn Practice
Lesson 4
4-4 Linear Regression
Learn Practice
Lesson 5
4-5 Inverses of Linear Functions
Learn Practice

4-2 Writing Equations in Standard and Point-Slope Forms

Property

Property

Examples

Property

Examples

Property

Examples

Unit 4: Creating Linear Equations

4-1 Writing Equations in Slope-Intercept Form

4-2 Writing Equations in Standard and Point-Slope Forms

4-3 Scatter Plots and Lines of Fit

4-4 Linear Regression

4-5 Inverses of Linear Functions

Lesson overview

Property

Property

Examples

Property

Examples

Property

Examples

Unit 4: Creating Linear Equations

4-1 Writing Equations in Slope-Intercept Form

4-2 Writing Equations in Standard and Point-Slope Forms

4-3 Scatter Plots and Lines of Fit

4-4 Linear Regression

4-5 Inverses of Linear Functions

4-1 Writing Equations in Slope-Intercept Form

4-2 Writing Equations in Standard and Point-Slope Forms

4-3 Scatter Plots and Lines of Fit

4-4 Linear Regression

4-5 Inverses of Linear Functions