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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 = ½
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

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