Lesson 6: Writing Equations in Slope-Intercept Form

Property

To write an equation from a graph in slope-intercept form $y = mx + b$:

1. Identify the y-intercept $b$ where the line crosses the y-axis
2. Find the slope $m = \frac{\text{rise}}{\text{run}}$ using two clear points on the line
3. Substitute $m$ and $b$ into $y = mx + b$

Examples

Property

The slope of a horizontal line, $y = b$, is 0.

Examples

Property

In a real-world context described by the equation $y = mx + b$:

• The slope ($m$) represents the rate of change. It tells you how much the dependent variable ($y$) changes for every one-unit increase in the independent variable ($x$).
• The y-intercept ($b$) represents the initial value or starting point. It is the value of the dependent variable ($y$) when the independent variable ($x$) is zero.

Examples