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−y1=m(x−x1)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−y1=m(x−x1)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 yy:

y−y1=m(x−x1)→y=mx−mx1+y1y - 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−y1=m(x−x1)y - y_1 = m(x - x_1) to standard form Ax+By=CAx + By = C:

  1. Distribute the slope on the right side
  2. Move all terms with variables to the left side
  3. Ensure A>0A > 0 and AA, BB, CC have no common factors

Examples

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−y1=m(x−x1)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−y1=m(x−x1)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 yy:

y−y1=m(x−x1)→y=mx−mx1+y1y - 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−y1=m(x−x1)y - y_1 = m(x - x_1) to standard form Ax+By=CAx + By = C:

  1. Distribute the slope on the right side
  2. Move all terms with variables to the left side
  3. Ensure A>0A > 0 and AA, BB, CC have no common factors

Examples