Question

Find the linear function graphs and give a partial interpretation the slope and vertical intercept

Answer 1

From the graph

We have the points

`(1,70),(3,170)`

First, we are to find the slope

To slope will be calculated using

`m=(y_2-y_1)/(x_2-x_1)`

From the given points we have

`\begin{gathered} x_1=1,x_2=3_{} \\ y_1=70,y_2=170 \end{gathered}`

Therefore, the slope is

`\begin{gathered} m=(170-70)/(3-1) \\ m=(100)/(2) \\ m=50 \end{gathered}`

Therefore, the slope is 50

Next we are to apply point slope form formula

The formula is given as

`y-y_1=m(x-x_1)`

By putting the values we have

We get the equation of the function as follows

`\begin{gathered} y-70=50(x-1) \\ y-70=50x-50 \\ y=50x-50+70 \\ y=50x+20 \end{gathered}`

Therefore, the linear function is y = 50x + 20

Finind the vertical intercept

The vertical intercept is the value of y at x = 0

Putting x = 0 in the linear function we have

`\begin{gathered} y=50(0)+20 \\ y=20 \end{gathered}`

The vertical intercept = 20