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Example 4.50 from Elementary Algebra, 4.5 Use the Slope–Intercept Form of an Equation of a Line
Use the Slope–Intercept Form of an Equation of a Line: example 4.50
Stella has a home business selling gourmet pizzas. The equation models the relation between her weekly cost, C, in dollars and the number of pizzas, p, that she sells.
ⓐ Find Stella’s cost for a week when she sells no pizzas.
ⓑ Find the cost for a week when she sells 15 pizzas.
ⓒ Interpret the slope and C-intercept of the equation.
ⓓ Graph the equation.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
ⓐ Find Stella's cost for a week when she sells no pizzas. Find C when . Simplify. Stella's fixed cost is $25 when she sells no pizzas. ⓑ Find the cost for a week when she sells 15 pizzas. Find C when . Simplify. Stella's costs are $85 when she sells 15 pizzas. ⓒ Interpret the slope and C-intercept of the equation. The slope, 4, means that the cost increases by $4 for each pizza Stella sells. The C-intercept means that even when Stella sells no pizzas, her costs for the week are $25. ⓓ Graph the equation. We'll need to use a larger scale than our usual. Start at the C-intercept (0, 25) then count out the rise of 4 and the run of 1 to get a second point.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Sam drives a delivery van. The equation models the relation between his weekly cost, C, in dollars and the number of miles, m, that he drives.
ⓐ Find Sam’s cost for a week when he drives 0 miles.
ⓑ Find the cost for a week when he drives 250 miles.
ⓒ Interpret the slope and C-intercept of the equation.
ⓓ Graph the equation.
How did it go?