Slope-intercept form is y = mx + b, where m is the slope and b is where the line crosses the y-axis.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
When to use it
It is the fastest form for graphing, because both features can be read straight off.
Point-slope form
y − y₁ = m(x − x₁) uses any point on the line, not only the intercept. It is the natural form when you are given a point and a slope.
Standard form
Ax + By = C treats x and y symmetrically. It handles vertical lines, which y = mx + b cannot.
Converting
Solving any form for y gives slope-intercept form. That single step converts all of them.
Same line, different clothes
All three describe the identical set of points. The choice is about convenience, never about correctness.
Three forms, three uses
Slope-intercept shows slope and starting value; point-slope suits a known point and slope; standard form suits systems and intercepts. All describe the same line and convert into each other.
Choose the form the data suits
Given a rate and a starting value, write slope-intercept directly. Given two points, compute the slope and use point-slope. Picking the right form first is usually the difference between two steps and six.
Graphing quickly
From slope-intercept, plot the intercept and step by the slope. From standard form, find both intercepts and join them. Both take seconds and beat building a table of values.
The line that fits no slope form
x = 3 has undefined slope and cannot be written as y = mx + b. Standard form accommodates it, which is one reason that form is kept alongside the more convenient ones.
Step 2: Try It Yourself
Tap and try it out.
The slope is 2: for every 1 across, the line goes 2 up.
Step 3: Watch an Example
One step at a time.
Watch Sana Write a Line
A line has slope 3 and passes through (2, 7).
- Step 1
She starts in point-slope form: y − 7 = 3(x − 2).
Step 4: Your Turn
Practice makes it stick.
The Intercept
Problem 1 of 2
y = 4x − 9. What is the y-intercept?
The Line
Problem 2 of 2
Slope 3 through (2, 7), written as y = 3x + b. What is b?
Write the Equation
1 of 8
y = 5x + 2. What is the slope?
2 of 8
y = −2x + 8. What is the y-intercept?
3 of 8
Slope 2 through (0, 5). What is b?
4 of 8
Slope 4 through (1, 10), as y = 4x + b. What is b?
5 of 8
2x + y = 7 solved for y gives y = −2x + c. What is c?
6 of 8
Which form can describe a vertical line? 1 slope-intercept, 2 standard.
7 of 8
Match each form with what it makes easiest.
Tap a card on the left to start.
8 of 8
Slope −3 through (2, 1), as y = −3x + b. What is b?
Step 5: Quick Check
Show what you know.
Question 1 of 2
Slope 2 through (3, 10), as y = 2x + b. What is b?
Question 2 of 2
How do you convert any form to slope-intercept form?
What You Learned
- Slope-intercept form is y = mx + b, best for graphing.
- Point-slope form builds a line from any point and a slope.
- Standard form handles vertical lines, which slope-intercept cannot.