Question

Given a linear function rule complete the table and find the following:

Answer 1

A) The rate, when we have the equation of a line, is equal to the slope.

If we have the equation of the line, the rate is:

`y=-5x+28\longrightarrow m=-5`

This means that for each unit of variation of x, y will variate -5 units.

The starting value is equal to the y-intercept, as it is the value of y when x=0.

In this case:

`y=-5x+28\longrightarrow y(0)=28`

We can complete the table by replacing x with the values and calculate for y:

`\begin{gathered} x=0\longrightarrow y=-5(0)+28=0+28=28 \\ x=1\longrightarrow y=-5(1)+28=-5+28=23 \\ x=2\longrightarrow y=-5(2)+28=-10+28=18 \\ x=3\longrightarrow y=-5(3)+28=-15+28=13 \end{gathered}`

B) In this case, applying what we do in the previous example, the equation, rate and y-intercept are:

`\begin{gathered} y=3x \\ \text{rate}\longrightarrow m=3 \\ \text{starting value}\longrightarrow y(0)=0 \end{gathered}`

We can find the values of the table as:

`\begin{gathered} x=0\longrightarrow y=3(0)=0 \\ x=1\longrightarrow y=3(1)=3 \\ x=2\longrightarrow y=3(2)=6 \\ x=3\longrightarrow y=3(3)=9 \end{gathered}`