Parents and Teachers: Support Ducksters by following us on Ducksters Facebook or Ducksters Twitter.
Ducksters Educational SiteDucksters Educational Site
History Biography Geography Science Games


Kids Math

Linear Equations - Slope Forms

This page assumes you have some basic knowledge of linear equations and slope. In the linear equations basics section we discussed the standard form of a linear equation where Ax + By = C.

There are other ways that linear equations can be written that can help provide useful information for graphing. They are called slope forms. There is the slope-intercept form and the point-slope form.

Slope-Intercept Form

The slope intercept form uses the following equation:

y = mx + b

In this equation, x and y are still the variables. The coefficients are m and b. These are numbers.

The advantage of putting a linear equation in this form is that the number for m equals the slope and the number for b equals the y-intercept. This makes the line the equation represents simple to graph.

m = slope
b = intercept

slope = (change in y) divided by the (change in x) = (y2 - y1)/(x2 - x1)

intercept = the point where the line crosses (or intercepts) the y-axis

Example Problems:

1) Graph the equation y = 1/2x + 1

From the equation y = mx + b we know that:

m = slope =
b = intercept = 1

1) Graph the equation y = 3x - 3

From the equation y = mx + b we know that:

m = slope = 3
b = intercept = -3

Point-Slope Form

The point-slope form of linear equation is used when you know the coordinates of one point on the line and the slope. The equation looks like this:

y - y1 = m(x - x1)

y1, x1 = the coordinates of the point you know
m = the slope, which you know
x, y = variables

Example Problems:

Graph a line that passes through the coordinate (2,2) and has a slope of 3/2. Write the equation in the slope-intercept form.

See the graph below. First we plotted the point (2,2) on the graph. Then we found another point using a rise of 3 and a run of 2. We drew a line between these two points.

To write this equation in slope-intercept form we use the equation:

y = mx + b

We already know that the slope (m) = 3/2 from the question. The y-intercept (b) we can see is at -1 from the graph. We can fill in m and b to get the answer:

y = 3/2x -1

Things to Remember

More Algebra Subjects
Algebra glossary
Linear Equations - Introduction
Linear Equations - Slope Forms
Order of Operations
Ratios, Fractions, and Percentages
Solving Algebra Equations with Addition and Subtraction
Solving Algebra Equations with Multiplication and Division

Back to Kids Math

Back to Kids Study


More polls

March is
Women's History Month

Be sure to check out our

Biographies of Women Leaders

About Ducksters Privacy Policy   

Follow us on Ducksters Facebook or Ducksters Twitter

This site is a product of TSI (Technological Solutions, Inc.), Copyright 2017, All Rights Reserved. By using this site you agree to the Terms of Use.