Question

Steven earns extra money babysitting. He charges $31.25 for 5 hours and $43.75 for 7 hours.

.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and
y represent the amount he charges.
The equation is y =?

Answer 1

Given:

Steven charges $31.25 for 5 hours and $43.75 for 7 hours.

To find:

The equation that represents the relationship.

Solution:

Let x represent the number of hours Steven babysits and y represent the amount he charges.

Then the two points on the function are (5,31.25) and (7,43.75). So, the equation of the line that passes through these two points is:

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

`y-31.25=(43.75-31.25)/(7-5)(x-5)`

`y-31.25=(12.5)/(2)(x-5)`

`y-31.25=6.25(x-5)`

On further simplification, we get

`y-31.25=6.25(x)-6.25(5)`

`y-31.25=6.25x-31.25`

`y=6.25x-31.25+31.25`

`y=6.25x`

Therefore, the required equation for the given situation is
`y=6.25x`.