Chapter 3: Q. 448R (page 356)

Katherine is a private chef. The equation $C = 6.5 m + 42$ models the relation between her weekly cost, C, in dollars and the number of meals, m, that she serves.
(a) Find Katherine's cost for a week when she serves no meals.
(b) Find the cost for a week when she serves 14 meals.
(c) Interpret the slope and C-intercept of the equation.
(d) Graph the equation.

Short Answer

Expert verified

(a) 42$

(b) 133$

C intercept is 42

(d)

Step by step solution

part (a) Step 1 Given information

Cost for a week when she serves no meals

C = 6.5 m + 42

part (a) Step 2 Solution

$C = 6.5 m + 42 C (0) = 6.5 \times 0 + 42 = 42$

Cost for a week when she serves no meals is $42 $$

part (b) Step 1 Given information

Cost for a week when she serves $14$ meals

$C = 6.5 m + 42$

part (b) Step 2 Solution

We have

$C = 6.5 m + 42 C (14) = 6.5 \times 14 + 42 = 91 + 42 = 133$

Cost for a week when she serves 14 meals is $133 $$

part (c) Step 1 Given information

Interpret the slope and C-intercept of the equation

$C = 6.5 m + 42$

part (c) Step 2 Solution

We have

$C = 6.5 m + 42$

Equation is of the form $y = m x + c$

Slope is $6.5$

C- intercept is $42$

part (d) Step 1 Given information

Graph the equation

$C = 6.5 m + 42$

part (d) Step 2 Solution

Graph is given by

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Short Answer

Step by step solution

part (a) Step 1 Given information

part (a) Step 2 Solution

part (b) Step 1 Given information

part (b) Step 2 Solution

part (c) Step 1 Given information

part (c) Step 2 Solution

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