Slope-Intercept Form — SAT Math Explained
The equation of a line written as y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
The Core Idea
This form immediately tells you two critical facts about a line: how steep it is (slope) and where it starts on the y-axis (intercept). It's the most efficient form for graphing lines quickly.
Key Vocabulary
The y-value where the line crosses the y-axis; where x = 0
The rate of change — tells you how the line tilts
y = mx + b — the standard algebraic form of a line
Ax + By = C — another way to write line equations, less visual but common in testing
How To Graph
1. Plot the y-intercept (0, b) as your starting point
2. Use the slope m = rise/run to find a second point (go up/down by rise, right by run)
3. Plot the second point
4. Draw a straight line through both points and extend with arrows
Converting Forms
Solve Ax + By = C for y by subtracting Ax and dividing by B
Distribute and simplify y - y₁ = m(x - x₁)
Find slope using two rows, then substitute one point to solve for b
Writing Equations From Information
Given slope and y-intercept: plug directly into y = mx + b
Given slope and one point: y = m(x) + b, plug in x and y, solve for b
Given two points: find slope first, then use one point to find b
Common Errors to Avoid
Confusing m and b — m is always the coefficient of x
Plotting the y-intercept on the x-axis by accident
Applying slope in the wrong direction (going left when you should go right)
Practice: Slope-Intercept Form
5 SAT-style questions. Select your answer and get an instant explanation.
What is the slope and y-intercept of y = 4x - 3?
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