Understanding Linear Equations and Their Graphs

This page introduces two key forms of linear equations: slope-intercept form and point-slope form. These forms are crucial for graphing linear equations step by step.

Slope-Intercept Form

The slope-intercept form is expressed as y = mx + b, where:

• m represents the slope
• b represents the y-intercept

Example: y + 2 = 2/3(x - 3)

This form is particularly useful when you need to quickly identify the slope and y-intercept of a line.

Point-Slope Form

The point-slope form is expressed as y₂ - y₁ = m(x₂ - x₁), where:

• (x₁, y₁) is a known point on the line
• m is the slope

Example: Given a point (-1, 3) and slope -4, the equation would be: y - 3 = -4(x + 1)

This form is helpful when you're given a point on the line and its slope.

Graphing a Line

To graph a line using the point-slope form:

1. Plot the given point
2. Use the slope to mark another point

Example: For the equation y + 3 = 2(x - 4), which passes through (4, -3) with a slope of 2:

1. Plot the point (4, -3)
2. Use the slope to find another point: moving right 1 unit and up 2 units

Highlight: Understanding these forms is crucial for graphing linear equations in two variables efficiently.