Graph Skills: Unit Four

The Slope and y-intercept in the Equation of a Line

Equation of a Line

The equation of a straight line is given on the right. In this equation:

"b" is the slope of the line, and
"a" is the y-intercept,

Each of these will be defined below. (NOTE: The equations of a line is frequently shown as y = m x + b.)

Equation for Pizza Example

Let's label the equation for our pizza example. The slope of the line tells us how much the cost of a pizza changes as the number of toppings change

Slope of Pizza Example
As you found in an earlier unit of this tutorial, the equation for our pizza example is:

y = 7.00 + .75 x
The slope in our pizza example is .75 (75 cents). In any equation of a straight line, the slope of the line is the constant that is multiplied by the x variable. (If you wish to review the definitions of constants and variables, return to the first unit.)

y-intercept of Pizza Example

In the equation y = a + b x, the constant labeled "a" is what is called the y-intercept. The y-intercept is the point at which the line crosses the y-axis. The y-intercept is the value of y when xis equal to zero.

Note that if x = 0, then y = a. When we use graphs, we call this point (0, a) the y-intercept.

In our pizza example, the equation of the relationship is given by y = 7.00 + .75 x.

The y-intercept occurs when there are no additional toppings (x = 0), which is the price of a plain pizza, or $7.00. As you can see, the point where the line crosses the y-axis is (0, 7). The y-intercept in this case is 7.

Now, let's look at a few more examples. In these we are simply trying to determine the slope and y-intercept from the equation of a line.

Example

y = 20 + 30 x.	y -intercept is 20 slope is 30
y = 4 - 10 x.	y -intercept is 4 slope is (-10)
y = .5 x + .66	y -intercept is .66 slope is .5

When you are sure you understand how to determine the y-intercept and slope of a line from its equation, do the practice exercise below.