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

Section 4.4: Graphing Linear Equations in Slope-Intercept Form

In this Grade 7 lesson from Big Ideas Math Advanced 2, students learn to identify the slope and y-intercept of a linear equation written in slope-intercept form (y = mx + b) and use those values to graph the line. The lesson covers key vocabulary including x-intercept, y-intercept, and slope-intercept form, and guides students through deriving the slope-intercept equation from the slope formula. Part of Chapter 4 on Graphing and Writing Linear Equations, this section builds the foundational skill of connecting an equation's structure to the visual behavior of its graph.

Section 1

x-intercept and y-intercept of a line

Property

The xx-intercept is the point (a,0)(a, 0) where the line crosses the xx-axis.

The yy-intercept is the point (0,b)(0, b) where the line crosses the yy-axis.

The xx-intercept occurs when yy is zero.

Section 2

Meaning of slope

Property

The slope of a line measures the rate of change of yy with respect to xx. In different situations, this rate might be interpreted as a rate of growth or a speed.

Examples

  • If a graph of distance (miles) vs. time (hours) has a slope of 5555, it represents an average speed of 55 miles per hour.
  • If a graph of cost (dollars) vs. weight (pounds) has a slope of 33, it means the price is 3 dollars per pound.

Book overview

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Chapter 4: Graphing and Writing Linear Equations

  1. Lesson 1

    Section 4.1: Graphing Linear Equations

  2. Lesson 2

    Section 4.2: Slope of a Line

  3. Lesson 3

    Section 4.3: Graphing Proportional Relationships

  4. Lesson 4Current

    Section 4.4: Graphing Linear Equations in Slope-Intercept Form

  5. Lesson 5

    Section 4.5: Graphing Linear Equations in Standard Form

  6. Lesson 6

    Section 4.6: Writing Equations in Slope-Intercept Form

  7. Lesson 7

    Section 4.7: Writing Equations in Point-Slope Form

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

x-intercept and y-intercept of a line

Property

The xx-intercept is the point (a,0)(a, 0) where the line crosses the xx-axis.

The yy-intercept is the point (0,b)(0, b) where the line crosses the yy-axis.

The xx-intercept occurs when yy is zero.

Section 2

Meaning of slope

Property

The slope of a line measures the rate of change of yy with respect to xx. In different situations, this rate might be interpreted as a rate of growth or a speed.

Examples

  • If a graph of distance (miles) vs. time (hours) has a slope of 5555, it represents an average speed of 55 miles per hour.
  • If a graph of cost (dollars) vs. weight (pounds) has a slope of 33, it means the price is 3 dollars per pound.

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

  2. Lesson 2

    Section 4.2: Slope of a Line

  3. Lesson 3

    Section 4.3: Graphing Proportional Relationships

  4. Lesson 4Current

    Section 4.4: Graphing Linear Equations in Slope-Intercept Form

  5. Lesson 5

    Section 4.5: Graphing Linear Equations in Standard Form

  6. Lesson 6

    Section 4.6: Writing Equations in Slope-Intercept Form

  7. Lesson 7

    Section 4.7: Writing Equations in Point-Slope Form