Is It a Function? Yes. Description: The value of y is equal to 2 times x plus 3. Equation: y=2x+3 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. Since each input x has only one output, the relation in the table is a function.
Words
Let's look for a pattern of change in the given table.
We can see that every time the x-values increase by 1, the y-values increase by 2. This might lead us to believe that the relationship is just 2 times x. However, we can see that this does not work by checking any of the points.
2* x&? =y
2* 0&≠3
2* 1&≠5
The values are 3 less than we need in each case. Therefore, we can say that the value of y is equal to 2 times x plus 3. Additionally, since y changes at a constant rate, we know that the function is linear. We will confirm this later when we graph the given points.
Equation
To describe the relation with an equation, let's translate our verbal description into algebraic terms.
The value ofy is equal to
2timesx plus3.
⇓
y = 2x +3
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 by using a straightedge. The relationship, therefore, is linear.
