Writing Equations in Slope-Intercept Form
is the most recognizable form of a linear equation. Given a slope and y-intercept — or two points — you can write the equation of any non-vertical line.
Introduction
You can calculate slope from two points. Now, combine slope with a y-intercept to write a full equation — one that lets you find the y-value for any x-value on that line.
Past Knowledge
Slope formula (3.2.1). Parallel/perpendicular slopes (3.2.2-3.2.3).
Today's Goal
Write the equation of a line in slope-intercept form given various information.
Future Success
Writing equations of parallel/perpendicular lines and coordinate proofs require this skill.
Key Concepts
Slope-Intercept Form
= slope, = y-intercept (where the line crosses the y-axis).
Three Common Scenarios
- Given m and b: Plug directly into .
- Given m and a point: Substitute the point to solve for b.
- Given two points: Find m first, then substitute one point to solve for b.
Interactive Diagram — Desmos Geometry
A line with its y-intercept highlighted and a rise/run triangle showing how slope connects to the equation.
Worked Examples
Given Slope and Y-Intercept
Slope = , y-intercept = 7. Write the equation.
Given Slope and a Point
Slope = , passes through . Write the equation.
Substitute into :
Parallel Line Through a Point
Write the equation of a line parallel to that passes through .
Parallel → same slope:
Common Pitfalls
Using the Point as the Y-Intercept
A point like is not the y-intercept unless . You must substitute the point into the equation and solve for b.
Real-Life Applications
Cost Modeling
A taxi charges $3.00 base fare plus $2.50 per mile. The equation models the total cost, where slope = rate per mile and y-intercept = base fare.
Practice Quiz
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