Understanding Slope-Intercept Form
The slope-intercept form y = mx + b is one of the most common ways to express a linear equation. In this form, m represents the slope (steepness) of the line, and b represents the y-intercept (where the line crosses the y-axis). This form makes it easy to quickly identify these key properties and graph the line.
Related Linear Equation Forms
Slope-Intercept Form
The most common form. m is slope, b is y-intercept.
y = mx + b
Point-Slope Form
Uses a known point (x1, y1) and slope m.
y - y1 = m(x - x1)
Standard Form
Ax + By = C where A, B, C are integers and A is positive.
Ax + By = C
Two-Point Formula
Derive slope from two points, then solve for b.
m = (y2-y1)/(x2-x1), b = y1-mx1
Intercept Form
Uses x-intercept (a) and y-intercept (b).
x/a + y/b = 1
Parallel / Perpendicular
Parallel lines have equal slopes. Perpendicular slopes multiply to -1.
m_perp = -1/m
How to Convert
From Two Points
- Calculate slope: m = (y2 - y1) / (x2 - x1)
- Plug slope and one point into y = mx + b
- Solve for b: b = y1 - m * x1
- Write the equation: y = mx + b
From Slope + Point
- You already know m (slope)
- Solve for b: b = y - mx
- Write the equation: y = mx + b
Key Takeaways
- The y-intercept b is the value of y when x = 0.
- The x-intercept is found by setting y = 0: x = -b/m.
- A horizontal line has slope 0: y = b.
- A vertical line cannot be expressed in slope-intercept form.