Question

You start a pet grooming service. You spend $30 on supplies. You plan to charge $5.00 to groom each pet. a. Write an equation in slope-intercept form to relate your profit ( y ) to the number of pets ( x ) you groom. b. Write the equation from part (a) in standard form. c. What are the x- and y-intercepts of the graph? d. What do the x- and y-intercepts mean in context of the problem?

Answer 1

To evaluate the profit we use the formula:
Profits=(total sales)-expenses
but:
total sales=(number of items)*(cost per item)
let the number of our items be x, the cost per item is$5, the initial expense is $30, the profit is y.
total sales will be:
sales=5×x=5x
thus the profit will be given by equation:
y=5x-30

b. Write the equation from part (a) in standard form.
rewriting the equation in standard form we shall have:
y=5x-30
the standard equation is given by:
-mx+y=c
thus writing our equation in this form we shall have:
-5x+y=-30

c] c. What are the x- and y-intercepts of the graph?
i] x-intercept
Using our standard equation
-5x-y=-30
to evaluate for the x-intercept we set y=0
thus our equation will be:
-5x=-30
hence
x=-30/-5=6


ii] y-intercept
again using the equation
-5x+y=-30
set x=0 and solve for y
y=-30

d] The x-intercept is minimum amount of items that have to be sold to break even. Y-intercept is the initial expenses.