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Basic Algebra
Slope-intercept Form: At a Glance

Introduction to Slope-intercept Form:

Another way to graph a line is to get it in slope-intercept form: y = mx + b, where

  • m is the slope of the line 
  • b is the y-intercept

Since we are given a point of the line, and the slope, we can find an infinite number of other points on the line and connect them.

Remember: slope (m) is equal to the (change in y) / (change in x). Slope = "rise over run"

Slope-intercept form of a line: y = mx + b

Let's examine how to graph one of these equations: y = 2x + 1.

This is in slope-intercept form, so we know that the number in front of x is the slope (2), and that 1 is the y-intercept.

Start by plotting the y-intercept.

graph

Next, since we know that the slope is 2, also known as 2/1, we know that another point will be two spaces up and one over (in the positive direction of course).

graph

Finally, connect these points.

graph

Look Out: when using slope-intercept form to graph lines, you must solve the equation for y, not x.

Slope-intercept Form Practice:

Example 1

Graph the equation y = -½x – 2.


Example 2

Graph the equation 4x + y = 7.


Example 3

Graph the equation 2y = x.


Example 4

Find the equation of the line in slope-intercept form.

graph


Exercise 1

Graph the equation: y = -x + 2.


Exercise 2

Graph the equation: y - ¼x = -1.


Exercise 3

Write the equation of this line in slope-intercept form:

graph


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