1. The slope for Sarah's Heavenly Cupcakes is $1.50, with a y-intercept of $1.50.
2. Frank's Pizzeria has a slope of $1.75 and a y-intercept of $10.
3. Marco's Computer Repair does not have a slope since the charges are fixed, but it has a y-intercept of $42.99.
When analyzing the businesses in the problem, we can identify the rate of change (slope) and the y-intercept (initial value) by looking at the pricing structures given for Sarah's Heavenly Cupcakes and Frank's Pizzeria.
For Sarah's business, the price increases by $1.50 for each additional cupcake; therefore, the slope is $1.50.
Since one cupcake costs $1.50, this is also the y-intercept, representing the fixed cost with zero units of the independent variable, i.e., without buying additional cupcakes.
In the case of Frank's Pizzeria, the equation provided is y = 10 + 1.75x, where x is the number of toppings, and y is the total cost.
The slope here is $1.75, indicating the additional cost per topping, and the y-intercept is $10, which is the cost of the medium pizza with no toppings.
Lastly, for Marco's Computer Repair, since the repair charges are fixed and do not change with time, there is no rate of change, and thus, the slope is 0.
The initial value or y-intercept is $42.99, the cost of the repair.
The probable question may be:
Do Now: Evaluating fun Nine friends just graduated from college with business degrees and are ready to start their own 1. Find businesses. The representations below describe each person's business.
1. Sarah's Heavenly Cupcakes
Number of cupcakes 1,2,3,4
price $1.50, $3.00, $4.50, $6.00
2. Frank's Pizzeria
y=10+1.75x
x= # of toppings
y= cost of a medium pizza
3. Marco's Computer Repair .
Marco charges $42.99 for a repair that takes 2 hours.
Determine the slope (rate of change) and y-intercept (initial value) for each representation