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What are the characteristics of a linear function?
Linear Function? Yes.
Description: The value of y is equal to 3 times x plus 5.
Equation: y=3x+5
Graph:
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.
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 | x | y | Change in y |
---|---|---|---|
0 | 5 | ||
+1 | 1 | 8 | +3 |
+1 | 2 | 11 | +3 |
+1 | 3 | 14 | +3 |
We can see that every time the x-values increase by 1, the y-values increase by 3. This might lead us to believe that the relationship is just 3 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. 3* x&? =y 3* 0&≠5 3* 1&≠8 Assuming y is equal to 3 times x, the values of y are 5 less than we need in each case. Therefore, we can say that the value of y is equal to 3 times x plus 5.
To describe the relation with an equation, let's translate our verbal description into algebraic terms. the value ofy is equal to 3timesxplus5 y = 3x+5
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.