Slope-Intercept Form
y = mx + bm = slopeb = y-intercept
Example: y = 2x + 3 has slope 2 and crosses the y-axis at (0, 3).
Best for graphing when you can see m and b.Formulas & graphing
Linear Equation Forms
A linear equation can be written in different forms. Each form describes the same kind of straight line but makes different information easier to see.
Equivalent equations:Different-looking equations are equivalent when they produce the same line and the same solutions.
Download Printable PDFStart with the meaning
What Is a Linear Equation?
A linear equation is an equation whose graph makes a straight line. Its rate of change, or slope, stays the same.
y = x + 1
The points line up in one straight line. Each time x increases by 1, y also increases by 1.
slope = y₂ − y₁x₂ − x₁
Why should I care?
Choosing the right form can make graphing, writing an equation, or finding missing information much easier.
Compare the forms
Three Ways to Write a Line
Point-Slope Form
y - y₁ = m(x - x₁)First find m with (y₂ − y₁)/(x₂ − x₁). Then use one known point for x₁ and y₁.
Example: slope 2 through (1, 4) becomes y − 4 = 2(x − 1).
Best when you know a point and the slope.Standard Form
Ax + By = CExample: 2x + y = 6. If x = 0, y = 6. If y = 0, x = 3.
Useful for finding where the line crosses both axes.See the same line in a different form
Rewrite 2x + y = 6 So y Is Alone
Step 1: Goal
To use y = mx + b, we need y by itself.
2x + y = 6
Step 2: Remove 2x
Subtract 2x from the left. Do the same on the right to keep both sides equal.
2x + y − 2x=6 − 2x
Step 3: Simplify
The 2x and −2x on the left cancel. Only y remains.
y = 6 − 2x
Step 4: Put x First
Write the x-term before the constant so it matches y = mx + b.
y = −2x + 6
m = −2, b = 6
m = −2, b = 6
Equation tool
Identify the Form
Enter a linear equation and see which form it uses.
Slope-Intercept Formy is by itself, so you can identify m and b.
Watch out
Common Mistakes
- Forgetting that y = x + 3 has a slope of 1.
- Reading the signs incorrectly in point-slope form.
- Moving a term without changing its sign.
Quick comparison
Choose the Helpful Form
Use slope-intercept for m and b, point-slope for one point and m, and standard form for intercepts or systems.
Your turn
10-Question Linear Forms Practice
Identify the form or find the requested part of the equation.
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