2.4 Linear Equations in Two Variables

Miller & Gerken, College Algebra 2e — Pages 240-255

Learning Objectives

  • Calculate slope from two points

  • Write equations in slope-intercept form

  • Write equations in point-slope form

  • Graph linear equations

Key Concepts

Slope Formula

\[m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{rise}}{\text{run}}\]

Forms of Linear Equations

Slope-Intercept Form

\(y = mx + b\)

Point-Slope Form

\(y - y_1 = m(x - x_1)\)

Standard Form

\(Ax + By = C\)

Special Cases

  • Horizontal line: \(y = k\) (slope = 0)

  • Vertical line: \(x = h\) (slope undefined)

Examples

Example 1. Example 1

Work through textbook example…​

Practice Problems

Problem 1 (p. XX, #YY)

Problem:

My Work:

Answer:

Section Summary

  1. Key point 1

  2. Key point 2

Study Notes

Personal observations…​

Next: 2.5 Linear Applications