Question

Drag each label to the correct location on the graph. Not all tiles will be used.

Darren hires a cab. The graph represents how much it will cost Darren in dollars in terms of the number of miles he travels in the cab. Identify the values and expressions represented in the graphed function.

Answer 1

Part 1)
`y=2.5x+3.5`

Part 2) The rate of change is
`2.5(\$)/(mile)`

Part 3) The initial value is $3.5

see the attached figure

Explanation:

Part 1) Find the equation of the line

Observing the graph

Identify the points (0,3.5) and (1,6)

calculate the slope

`m=(6-3.5)/(1-0)=2.5(\$)/(mile)`

Find the equation of the line

`y=mx+b` --->equation of the line into slope intercept form

we have

`m=2.5\\ b=3.5`

substitute

`y=2.5x+3.5`

Part 2) Find the rate of change

we know that

The rate of change of the graph is equal to the slope of the line

the slope of the line is
`m=2.5(\$)/(mile)`

therefore

The rate of change is
`2.5(\$)/(mile)`

Part 3) Find the initial value

we know that

The initial value of the function is the y-intercept, is the value of y when the value of x is equal to zero

In this problem is the cost when the distance is equal to zero

The y-intercept is the point (0,3.5)

therefore

The initial value is $3.5