Question

How do i write the equations and plot both of them on a graph.

Babysitting:
Suzie and Brenan babysit for two different families to make a little extra money. Suzie's pay is $8 per hour as well as $10 extra per week as a retainer. Brenan's pay is determined by how many hours Brenan works a week. Plus, Brenan receives a set weekly stipend for gas because the family lives in the country. Brenan has been babysitting for the past four weeks, and the following chart shows how much he was paid each week.

Week Hours Worked Pay (dollars)
1 6 60
2 15 132
3 21 180
4 12 108

Write a separate linear equation for both Suzie and Brenan that relate their babysitting hours (h) to their weekly pay.

Answer 1

Suzie's linear equation for weekly pay is Pay = (8 X hours) + 10, and Brenan's is Pay = (9 X hours) + 6. To plot these, draw lines with their respective slopes and y-intercepts on a graph.

Step-by-step explanation:

To find the linear equations for Suzie's and Brenan's weekly pay, we need to establish the relationship between the hours worked (the independent variable) and the weekly pay (the dependent variable).

Brenan's pay consists of an hourly rate plus a weekly stipend for gas. To determine Brenan's hourly rate and stipend, we'll use the given data: Week 1: 6 hours, $60 pay Week 2: 15 hours, $132 pay Week 3: 21 hours, $180 pay Week 4: 12 hours, $108 pay Using any two data points, we can determine the hourly rate by subtracting the total pay and dividing by the number of hours. We'll take Week 1 and Week 4: For Week 1: $60 = (hourly rate × 6) + stipend For Week 4: $108 = (hourly rate × 12) + stipend By solving these equations simultaneously, we find Brenan's hourly rate is $9 and the weekly stipend for gas is $6.

Hence, Brenan's equation of pay is: Pay = (9 × hours) + 6 To plot the graphs of these equations on a coordinated plane, simply draw a line with a slope equal to the hourly rate and a y-intercept equal to the weekly retainer or stipend.