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

4-1 Writing Equations in Slope-Intercept Form

In this Grade 9 lesson from California Reveal Math Algebra 1, students learn to write equations of a line in slope-intercept form (y = mx + b) given the slope and one point or given two points. The lesson covers finding the y-intercept by substituting known coordinates into the slope-intercept equation, as well as applying the slope formula when only two points are provided. Real-world contexts, such as oven temperature changes, help students connect linear equations to practical situations.

Section 1

Slope-Intercept Form: y = mx + b

Property

The slope-intercept form of a linear equation is:

y = mx + b

Section 2

Equation from slope and y-intercept

Property

We can easily determine the slope and intercept of a line if the equation was written in slope-intercept form, $y = mx + b$ .
Now, we will do the reverse—we will start with the slope and y-intercept and use them to find the equation of the line.
To find an equation of a line with a given slope and y-intercept, substitute the slope ( $m$ ) and the y-coordinate of the y-intercept ( $b$ ) into the slope-intercept form, $y = mx + b$ .

Examples

Find the equation of a line with slope 4 and y-intercept $(0, 2)$ . We substitute $m=4$ and $b=2$ into $y = mx + b$ to get the equation $y = 4x + 2$ .

Find the equation of a line with slope $-5$ and y-intercept $(0, -1)$ . We substitute $m=-5$ and $b=-1$ into $y = mx + b$ to get the equation $y = -5x - 1$ .

Section 3

Calculating Slope from Two Points

Property

The slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the slope formula:

m = \frac{y_2 - y_1}{x_2 - x_1}

Examples

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Unit 4: Creating Linear Equations

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

Expand to review the lesson summary and core properties.

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Section 1

Slope-Intercept Form: y = mx + b

Property

The slope-intercept form of a linear equation is:

y = mx + b

Section 2

Equation from slope and y-intercept

Property

Examples

Find the equation of a line with slope 4 and y-intercept $(0, 2)$ . We substitute $m=4$ and $b=2$ into $y = mx + b$ to get the equation $y = 4x + 2$ .

Find the equation of a line with slope $-5$ and y-intercept $(0, -1)$ . We substitute $m=-5$ and $b=-1$ into $y = mx + b$ to get the equation $y = -5x - 1$ .

Section 3

Calculating Slope from Two Points

Property

The slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the slope formula:

m = \frac{y_2 - y_1}{x_2 - x_1}

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 1Current
4-1 Writing Equations in Slope-Intercept Form
Learn Practice
Lesson 2
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

Slope-Intercept Form: y = mx + b

Property

The slope-intercept form of a linear equation is:

y = mx + b

Section 2

Equation from slope and y-intercept

Property

Examples

Find the equation of a line with slope 4 and y-intercept $(0, 2)$ . We substitute $m=4$ and $b=2$ into $y = mx + b$ to get the equation $y = 4x + 2$ .

Find the equation of a line with slope $-5$ and y-intercept $(0, -1)$ . We substitute $m=-5$ and $b=-1$ into $y = mx + b$ to get the equation $y = -5x - 1$ .

Section 3

Calculating Slope from Two Points

Property

The slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is calculated using the slope formula:

m = \frac{y_2 - y_1}{x_2 - x_1}

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 1Current
4-1 Writing Equations in Slope-Intercept Form
Learn Practice
Lesson 2
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

4-1 Writing Equations in Slope-Intercept Form

Property

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

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