## 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 equation 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 x is 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

Determine the slope and y-intercept for the line given by each equation.

 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.    [practice] [additional practice] [table of contents] [next unit]