Applying the Concepts and SkillsAir-Conditioning Repairs. Richard’s Heating and Cooling in Prescott, Arizona, charges $55 per hour plus a $30 service charge. Let x denote the number of hours required for a job, and let y denote the total cost to the customer.a. Find the equation that expresses y in terms of x.b. Determine b0 and b1.c. Construct a table similar to Table on page 620 for the x-values 0.5, 1, and 2.25 hours.d. Draw the graph of the equation that you determined in part (a) by plotting the points from part (c) and connecting them with a line.e. Apply the graph from part (d) to estimate visually the cost of a job that takes 1.75 hours. Then calculate that cost exactly by using the equation from part (a).TABLETimes and costs for five word-processing jobs Time (hr) Cost (S) x y 5.0 125 7.5 175 15.0 325 20 425 22.5 475
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Applying the Concepts and Skills
Air-Conditioning Repairs. Richard’s Heating and Cooling in Prescott, Arizona, charges $55 per hour plus a $30 service charge. Let x denote the number of hours required for a job, and let y denote the total cost to the customer.
a. Find the equation that expresses y in terms of x.
b. Determine b0 and b1.
c. Construct a table similar to Table on page 620 for the x-values 0.5, 1, and 2.25 hours.
d. Draw the graph of the equation that you determined in part (a) by plotting the points from part (c) and connecting them with a line.
e. Apply the graph from part (d) to estimate visually the cost of a job that takes 1.75 hours. Then calculate that cost exactly by using the equation from part (a).
TABLE
Times and costs for five word-processing jobs
| Time (hr) | Cost (S) |
| x | y |
| 5.0 | 125 |
| 7.5 | 175 |
| 15.0 | 325 |
| 20 | 425 |
| 22.5 | 475 |
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