Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
2. Direct Variation
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Exercise 40 Page 305

Practice makes perfect
a We have been given four direct variation equations and are asked to graph them in the same coordinate plane. Let's start with y=x. In order to graph y=x, we will create a table of values.
x y
-1 -1
0 0
1 1
2 2

If we plot these points on the coordinate plane and connect them, we will have the graph of y=x.

We can apply the same process to the other direct variation equations, y=2x, y=3x, and y=4x.

b Let's first make a table to consider the constant of variation for each equation.
Equation Constant of Variation
y=( 1)x 1
y= 2x 2
y= 3x 3
y= 4x 4

With this information we will examine the graph in Part A. We can see from the graph that as the constant of variation increases the slopes of the graphs become more steep.

c If we have the direct variation equation y= 12x, we can predict that the graph of it would appear less steep when compared to the previous graphs. This is because its constant of variation is less than the other equations. Let's check!

As we can see, the graph of the function is increasing at a much slower rate than the other functions.