Question

On Friday, Jessica babysat for 3 hours and earned $27. On Saturday, Jessica babysat for 6 hours and earned $54. On Friday, Jessica babysat for 7 hours and earned $63. Write an equation to represent her earnings if x represents hours and y represents earnings

Answer 1

y = 9x

Explanation:

We can make the x-values represent how many hours Jessica babysat, and the y-values represent how much money she earned each day.

We have these points:

• (3, 27)
• (6, 54)
• (7, 63)

The days of the week she worked do not matter in this problem. We are just trying to find the association between hours worked and money earned.

We can start by finding the slope of the line by using two of the points. I will be using (3, 27) and (6, 54).

The slope formula is
`\displaystyle m = (y_2-y_1)/(x_2-x_1)`.

Substitute these two points into the formula:

• 
  `\displaystyle m = (54-27)/(6-3)`
• 
  `\displaystyle m = (27)/(3)`
• 
  `m=9`

The slope of the line is m = 9.

Now, we can use the point-slope equation to find the equation of the line that represents Jessica's earnings.

Point-slope equation:
`y-y_1=m(x-x_1)`.

Substitute the slope m = 9 and the point (3, 27) into the equation.

• 
  `y-(27)=9(x-(3))`
• 
  `y-27=9(x-3)`
• 
  `y-27=9x-27`
• 
  `y=9x`

The equation y = 9x represents Jessica's earnings, where x represents hours and y represents earnings.