Linear Function? Yes. Description: The value of y is equal to - 117 times x plus 11.2. Equation: y=- 117x+11.2 Graph:
Practice makes perfect
The graph of a linear function is a straight, non-vertical line. To determine whether the relation in the table is a linear function, let's first confirm that the relation is a function.
Words
Since each input x has only one output, the relation in the table is a function. Let's look for a pattern of change in the given table.
Change in x
Miles Traveled, x
Gallons of Gas, y
Change in y
0
11.2
+17
17
10.2
-1
+17
34
9.2
-1
+17
51
8.2
-1
We can see that every time the x-values increase by 17, the y-values decrease by 1. This might lead us to believe that the relationship is just - 117 times x. However, by testing the values of x with this relationship, we can see that the resulting values of y are not equal to the given values.
-1/17* x&? =y
-1/17* 0&≠11.2
-1/17* 17&≠10.2
Assuming y is equal to - 117 times x, the values of y are 11.2 less than we need in each case. Therefore, we can say that the value of y is equal to - 117 times x plus 11.2.
Equation
To describe the relation with an equation, let's translate our verbal description into algebraic terms.
the value ofy is equal to
- 117timesxplus11.2
y = -1/17x+11.2
Graph
Now, let's graph the points. By doing so, we will also be able to determine if the relationship is a linear function.
The graph of a linear function is a straight, non-vertical line. Now that we have graphed the given points, we can see that they are able to be connected with a straight line. The relationship is therefore linear.
