The lesson
This lesson teaches Slope-Intercept Form. Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
y = mx + b
In slope-intercept form, m is the slope and b is the y-intercept (where the line crosses the y-axis).
When you study y = mx + b, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
Graphing from y = mx + b
When you study graphing from y = mx + b, slow down and write one example in your notebook without looking at the screen. That active step is what turns reading into learning.
- 1Plot the y-intercept (0, b) first.
- 2Use the slope as rise over run to plot a second point.
- 3Draw a line through the two points.
Graph y = 2x + 3.
- 1y-intercept is 3, so plot (0, 3).
- 2Slope 2 = 2/1: go up 2 and right 1 to (1, 5).
- 3Draw the line through (0, 3) and (1, 5).
Why this matters
Slope-Intercept Form shows up constantly in read slope and y-intercept straight from y = mx + b. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- y = mx + b
- Graphing from y = mx + b
- Plot the y-intercept (0, b) first.
- Use the slope as rise over run to plot a second point.
- Draw a line through the two points.
Video walkthrough
Practice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfIn y = 5x − 2, what are the slope and y-intercept?
Step-by-step solution
- 1m is the coefficient of x: slope = 5.
- 2b is the constant term: y-intercept = −2.
- 3Slope 5, y-intercept −2.
Exercise 2
Try it yourselfWrite an equation with slope −2 and y-intercept 7.
Step-by-step solution
- 1m = −2 and b = 7.
- 2y = mx + b → y = −2x + 7.
- 3Equation: y = −2x + 7.
Exercise 3
Try it yourselfGraph y = (1/2)x + 4. What point is the y-intercept?
Step-by-step solution
- 1Set x = 0: y = 4.
- 2Plot (0, 4) on the y-axis.
- 3y-intercept: (0, 4).
Exercise 4
Try it yourselfA line has slope 3 and passes through (0, −1). Write its equation.
Step-by-step solution
- 1Slope m = 3, y-intercept b = −1.
- 2y = 3x − 1.
- 3Equation: y = 3x − 1.
Exercise 5
Try it yourselfRewrite 2x + y = 10 in slope-intercept form.
Step-by-step solution
- 1Subtract 2x from both sides: y = −2x + 10.
- 2Slope is −2, y-intercept is 10.
- 3y = −2x + 10.
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Slope-Intercept Form
Question 1 of 4
In y = -3x + 5, what is the slope?