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?
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.
