Question

Slope and rate of change
help please on card 7 an 8

Answer 1

Card 7

The hourly rate of change/slope is $75 per hour.

Card 8

Frastastic is charging $0.48 per ounce.

Explanation:

Card 7

Lets take the set up fee as "$
`s`" and,

Hourly rate as $
`x`per hour.

Now we can write equations for 3 hour event and 5 hour event.

`s+3x=275` <------- (1)

`s+5x=425` <------- (2)

Now we need to solve the simultaneous equations to find
`s` and
`x`.

Subtract (1) from (2)

⇒
`s+5x-(s+3x)=425-275`

`s+5x-s-3x=150`

`2x=150`

`x=75`

So the hourly rate of change/slope is $75 per hour.

Therefore, Raymond is right.

Card 8

You can take Amount (oz) as x values and Cost as y values and plot a graph.

Then the Slope of the graph will give you the rate Frastastic is charging per yogurt.

Slope of a linear graph is given by the following equation;

Slope(m)=
`\frac{y_(1)-{y_(2)}}  {x_(1)-x_(2)   }`

Slope(m)=
`(6.72-2.4)/(14-5)`

Slope(m)=
`(4.32)/(9)`

Slope(m)=
`0.48`

Therefore, Frastastic is charging $0.48 per ounce.

This is less than $0.50 per ounce charged by Fromazing. Therefore, Sterling is right.