You can use the point-slope form to find an equation of a line if you know its slope and a point on the line. You can convert point-slope form to slope-intercept form by simplifying. Answer the following questions. Click “Submit” when finished.

This table of values describes a line. Can we find an equation for this line? To find the slope, we need to find the ratio of the difference between the <EQUATION> to the difference between the <EQUATION> of the points on the line. The points we know are <EQUATION> and <EQUATION>. So, the slope of the line is <EQUATION>, which is <EQUATION>, or <EQUATION>.

Now, we can use the point-slope equation and either of the points to find an equation of the line. For example, if we use the point <EQUATION>, we get <EQUATION>. Simplifying this equation we get <EQUATION>. We would have found the same slope-intercept equation if we had instead used the point <EQUATION>. So the line that passes through the points <EQUATION> and <EQUATION> has slope <EQUATION> and <EQUATION>.

Another way to find the equation of the line after you find the slope is to use the slope-intercept form. We found that the slope is <EQUATION>, so we can substitute <EQUATION> in the equation. Then we can choose one of the points on the line and substitute <EQUATION> with the <EQUATION> - and <EQUATION> of the point.

Now we can solve for <EQUATION>. Then, substituting for <EQUATION> in the equation <EQUATION>, we again find that the slope-intercept form of the equation of this line is <EQUATION>.

Find the slope-intercept form of the equation of the line through the points <EQUATION> and <EQUATION>. Click “Submit” when finished.

Consider the points <EQUATION> and <EQUATION>. Let’s find an equation of the line through these points. First, we'll find the slope. To find the slope of the line, we need to find the ratio of the difference between the <EQUATION> to the difference between the <EQUATION> of the points on the line. So, the slope of the line is <EQUATION>, or <EQUATION>. But we can’t divide by zero, so <EQUATION> is undefined. That is, the slope of the line is undefined.

If we plot these points on the coordinate plane, we see that the line through them is a vertical line. The slope of a vertical line is undefined. Notice that the <EQUATION> of both points on the line is <EQUATION>. In fact, the <EQUATION> of the points on this line is <EQUATION>. So, the equation of the line is <EQUATION>.

A sporting goods store sells cans of tennis balls. They have noticed that if they sell the cans for <EQUATION>, they will sell <EQUATION> cans each week. However, if they raise the price to <EQUATION>, they will only sell <EQUATION> cans of tennis balls. If the relationship between the price of the cans and the number of cans sold is linear, how many cans of tennis balls they will sell at <EQUATION> per can?

Let’s put this data in a table and sketch a graph. Let <EQUATION> be the price of each can and let <EQUATION> be the number of cans that are sold. Then, when <EQUATION> is <EQUATION> is <EQUATION>, and when <EQUATION> is <EQUATION> is <EQUATION>.

<EQUATION> is the price, so <EQUATION> is never negative. Similarly, <EQUATION> is the number of cans, so <EQUATION> is never negative. Therefore, the horizontal and vertical axes only need to show positive numbers. To predict the number of cans that will be sold at the price of <EQUATION>, we need to find an equation for the line that passes through the two known points. First, we need to find the slope of the line.

The slope of this line is <EQUATION>, which is <EQUATION>, or <EQUATION>. Now, we can use the point-slope form to find an equation of the line. Using the point <EQUATION> and simplifying, we find that an equation of the line is <EQUATION>. Drawing this line, we see that it does pass through the two points given. The slope of the line is negative and its <EQUATION> is a positive number.

To predict the number of cans sold at the price of <EQUATION>, we need to find the <EQUATION> that corresponds to an <EQUATION> of <EQUATION>. That is, we should substitute <EQUATION> in <EQUATION> and solve for <EQUATION>. So, <EQUATION> is <EQUATION> or <EQUATION>. This means that the store will sell <EQUATION> cans of tennis balls each week if it sells them at a price of <EQUATION> per can.

What price should the store charge for each can of tennis balls if they want to sell <EQUATION> cans each week? Click “Submit” when finished.

Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education