Learn on PengiBig Ideas Math, Advanced 2Chapter 4: Graphing and Writing Linear Equations

Section 4.7: Writing Equations in Point-Slope Form

In this Grade 7 lesson from Big Ideas Math Advanced 2, students learn to write linear equations in point-slope form, y − y₁ = m(x − x₁), using a given slope and a point on the line. The lesson covers how to apply point-slope form when working with two points by first calculating slope using the slope formula, then converting to slope-intercept form. Part of Chapter 4 on Graphing and Writing Linear Equations, the lesson builds students' ability to represent real-world situations as linear equations.

Section 1

Point-slope form of an equation

Property

The point-slope form of an equation of a line with slope mm and containing the point (x1,y1)(x_1, y_1) is

y−y1=m(x−x1)y - y_1 = m(x - x_1)

We can use the point-slope form of an equation to find an equation of a line when we are given the slope and one point.

Examples

  • A line has a slope of 5 and passes through the point (2,8)(2, 8). Its equation in point-slope form is y−8=5(x−2)y - 8 = 5(x - 2).
  • A line has a slope of −34-\frac{3}{4} and passes through the point (−4,1)(-4, 1). Its equation is y−1=−34(x−(−4))y - 1 = -\frac{3}{4}(x - (-4)), which simplifies to y−1=−34(x+4)y - 1 = -\frac{3}{4}(x + 4).

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

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

Book overview

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Chapter 4: Graphing and Writing Linear Equations

  1. Lesson 1

    Section 4.1: Graphing Linear Equations

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  2. Lesson 2

    Section 4.2: Slope of a Line

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  3. Lesson 3

    Section 4.3: Graphing Proportional Relationships

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  4. Lesson 4

    Section 4.4: Graphing Linear Equations in Slope-Intercept Form

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  5. Lesson 5

    Section 4.5: Graphing Linear Equations in Standard Form

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  6. Lesson 6

    Section 4.6: Writing Equations in Slope-Intercept Form

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  7. Lesson 7Current

    Section 4.7: Writing Equations in Point-Slope Form

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Lesson overview

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Section 1

Point-slope form of an equation

Property

The point-slope form of an equation of a line with slope mm and containing the point (x1,y1)(x_1, y_1) is

y−y1=m(x−x1)y - y_1 = m(x - x_1)

We can use the point-slope form of an equation to find an equation of a line when we are given the slope and one point.

Examples

  • A line has a slope of 5 and passes through the point (2,8)(2, 8). Its equation in point-slope form is y−8=5(x−2)y - 8 = 5(x - 2).
  • A line has a slope of −34-\frac{3}{4} and passes through the point (−4,1)(-4, 1). Its equation is y−1=−34(x−(−4))y - 1 = -\frac{3}{4}(x - (-4)), which simplifies to y−1=−34(x+4)y - 1 = -\frac{3}{4}(x + 4).

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

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

Book overview

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

Continue this chapter

Chapter 4: Graphing and Writing Linear Equations

  1. Lesson 1

    Section 4.1: Graphing Linear Equations

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  2. Lesson 2

    Section 4.2: Slope of a Line

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  3. Lesson 3

    Section 4.3: Graphing Proportional Relationships

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  4. Lesson 4

    Section 4.4: Graphing Linear Equations in Slope-Intercept Form

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  5. Lesson 5

    Section 4.5: Graphing Linear Equations in Standard Form

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  6. Lesson 6

    Section 4.6: Writing Equations in Slope-Intercept Form

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  7. Lesson 7Current

    Section 4.7: Writing Equations in Point-Slope Form

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