The equation of a straight line is given on the right. In this equation:
Each of these will be defined below. (NOTE: The equation of a line is frequently shown as y = m x + b.) |
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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 |
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As you found in an earlier unit of this tutorial, the
equation for our pizza example is:
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.)
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. |
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In our pizza example, the equation of the relationship is given by: 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. |
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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.
Determine the slope and y-intercept for the line given by each equation.
y = 20 + 30 x y -intercept is 20
slope is 30y = 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] |