If the relationship between the dependent and independent variables is linear, the rate of change is the same between any two sets of variables along the line. The change in the dependent variable is , or 30, and the change in the independent variable is , or 3. In a linear relationship, the rate of change is constant. The slope of a line can also be described by its direction. In the relationship of the paycheck and number of hours worked, the line rises from left to right. The more hours worked, the higher the paycheck, with a positive slope.
Suppose a plane is landing. The relationship between its elevation and the time from its highest altitude is a falling line from left to right, a negative slope. If the relationship is a horizontal line, so that no change occurs, the slope is zero.
However, if the relationship is a vertical line, the slope is undefined. It is also not a function, as there are multiple values of y for one value of x. The slope of a line is usually represented by the variable m. It is expressed by the ratio of the difference in value of y variables to the difference in value of x variables. Show related SlideShares at end. WordPress Shortcode. Next SlideShares. Download Now Download to read offline and view in fullscreen. Download Now Download Download to read offline.
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No notes for slide. We can't count the rise over the run like we did in the calculating slope lesson because our units on the x and y axis are not the same. In most real life problems, your units will not be the same on the x and y axis. So, we need another method! We will need to use a formula for finding slope given two points. If you've never used this formula before, please visit our page on using the slope formula. Let's take a look at John's graph again.
John would like to find out how much money he saved per month for the year. In other words, John wants to know the rate of change per month. We are finding out how much John's account changes per month on average.
We can now use the slope formula to find the slope of the line. The slope is the rate of change from one month to the next. Find the average annual rate of change in dollars per year in the value of the house.
Round your answer to the nearest dollar. For this problem, we don't have a graph to refer to in order to identify the two ordered pairs.
Therefore, we must find two ordered pairs within the context of this problem. I am given information about the year in which Linda purchased a house and the amount that the house is worth. Since these two items are related, I can write them as an ordered pair.
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