Slope-Intercept Form Explained

Slope-intercept form is one of the most useful ways to write a linear equation because it tells you how to graph the line quickly.

Quick idea

In y = mx + b, m is the slope and b is the y-intercept.

Steps

1. Look for the number multiplying x. That is the slope.
2. Look for the constant added or subtracted. That is the y-intercept.
3. Start the graph at the y-intercept.
4. Use the slope to find another point.

Worked example

Identify the slope and y-intercept of y equals negative 3x plus 4.

Full solution

Step-by-step walkthrough

Step 1

The coefficient of x is -3, so the slope is -3.

Step 2

The constant is 4, so the line crosses the y-axis at 4.

Step 3

A negative slope means the line falls from left to right.

Common mistake

The y-intercept is not always the last number if the equation is not solved for y. Rewrite first if needed.

Practice problems

1. Find m and b in y = 5x - 2.
2. Find m and b in y = -x + 7.
3. Find m and b in y = 3/4 x.

Answers

1. m = 5, b = -2
2. m = -1, b = 7
3. m = 3/4, b = 0

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• What Is Slope? Rise Over Run Explained
• How to Graph a Linear Equation
• How to Solve Systems of Equations by Substitution