Learn Before
Interpreting the Slope and -Intercept of
Stella runs a home business selling gourmet pizzas. Her weekly cost is modeled by the linear equation , where is the weekly cost in dollars and is the number of pizzas sold. Although the equation uses and instead of and , it is still in slope-intercept form.
ⓐ Find when :
Stella's fixed cost is $25 per week when she sells no pizzas.
ⓑ Find when :
Stella's cost is $85 when she sells 15 pizzas.
ⓒ Interpret the slope and -intercept:
- The slope is , which means the cost increases by $4 for each pizza Stella sells. This is the variable cost per pizza.
- The -intercept is , which means that even when Stella sells no pizzas, her weekly costs are $25. This is the fixed cost.
ⓓ Graph the equation:
Because the -intercept is at , a larger scale than the standard to grid is needed. Start at the -intercept , then count out a rise of and a run of to locate a second point. Draw a straight line through the two points. The line passes through and .
This example shows how the slope-intercept form applies to a business cost equation: the slope represents the per-unit variable cost, and the vertical-axis intercept represents the fixed cost.
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Learn After
In the linear equation C = 4p + 25, which models the weekly cost for Stella's pizza business, what does the constant value 25 represent?
In Stella's pizza business, the weekly cost is modeled by the equation , where is the weekly cost and is the number of pizzas sold. Match each component of the equation to its corresponding business definition.
Stella uses the equation to model her weekly business costs, where is the total cost and is the number of pizzas sold. Based on this model, if Stella sells zero pizzas in a week, her total cost for that week will be $____.
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Interpreting Variable Cost in a Linear Equation
To create a visual budget for her gourmet pizza business, Stella needs to graph her weekly cost equation: . Arrange the following steps in the correct order to graph this line using the slope and intercept.
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Business Cost Interpretation for Stella's Pizza Model
Stella uses the linear equation to model her weekly pizza business costs, where is the total cost and is the number of pizzas sold. In this model, what is the mathematical term for the value 25, which represents her fixed weekly costs?
Stella models her weekly business costs with the equation , where is the total cost and is the number of pizzas sold. Which ordered pair represents the point where Stella's cost graph crosses the vertical axis (-axis)?