Linear Function? Yes. Description: The value of y is equal to 1.29 times x plus 52.07. Equation: y=1.29x+52.07 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
Number of Soup Cans, x
Total Bill, y
Change in y
0
$52.07
+1
1
$53.36
+1.29
+1
2
$54.65
+1.29
+1
3
$55.94
+1.29
We can see that every time the x-values increase by 1, the y-values increase by 1.29. This might lead us to believe that the relationship is just 1.29 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.
1.29* x&? =y
1.29* 0&≠52.07
1.29* 1&≠53.36
Assuming y is equal to 1.29 times x, the values of y are 52.07 less than we need in each case. Therefore, we can say that the value of y is equal to 1.29 times x plus 52.07.
Equation
To describe the relation with an equation, let's translate our verbal description into algebraic terms.
the value ofy is equal to
1.29timesxplus52.07
y = 1.29x+52.07
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.
