Slope-Intercept Form

The most common form for linear equations is slope-intercept form:

$y = mx + b$

Where:

• $m$ = slope (steepness of the line)
• $b$ = y-intercept (where the line crosses the y-axis)

Understanding Slope

Slope measures how steep a line is:

$m = \frac{\text{rise}}{\text{run}} = \frac{\text{change in } y}{\text{change in } x}$

Types of Slope

Slope	Description	Line Goes
Positive	Line goes up	↗
Negative	Line goes down	↘
Zero	Horizontal line	→
Undefined	Vertical line	↑

Calculating Slope

Between two points $(x_1, y_1)$ and $(x_2, y_2)$:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Example: Find slope between $(2, 3)$ and $(5, 9)$ $m = \frac{9 - 3}{5 - 2} = \frac{6}{3} = 2$

Understanding Y-Intercept

The y-intercept is where the line crosses the y-axis.

• It's the value of $y$ when $x = 0$
• Written as the point $(0, b)$

Examples

Example 1: $y = 2x + 3$

• Slope: $m = 2$ (rise 2, run 1)
• Y-intercept: $b = 3$ (crosses at $(0, 3)$)

Example 2: $y = -\frac{1}{2}x + 4$

• Slope: $m = -\frac{1}{2}$ (down 1, right 2)
• Y-intercept: $b = 4$ (crosses at $(0, 4)$)

Graphing Using Slope-Intercept

To graph $y = 2x + 1$:

1. Plot the y-intercept $(0, 1)$
2. From there, use slope: rise 2, run 1
3. Plot second point $(1, 3)$
4. Draw a line through both points