Your profits will not be positive until you have been paid back the purchase of supplies.
B
b
Draw the graph by using the slope and the y-intercept of the equation found in Part A. Find the intercepts by looking at the graph.
A
a
y=5x-30
B
b
x-intercept: 6
y-intercept: -30 Graph:
Practice makes perfect
a
We bought supplies before we groomed any pets, so we are starting off $30 in debt. Let's think about this in terms of the number of pets groomed x and our total profit y. When we have groomed 0 pets, our total profit is -$30.
Groomed pets: & x=0
Profit is-$30: & y=-30
Because this relation has an x-value of 0, we know that this is going to be the y-intercept of our equation. If we want to write the equation in slope-intercept form, the y-value of the relation is the value of b.
b= -30
We plan on charging $ 5 for each groomed pet, so we can write an expression for the profits.
5x
In this expression 5 can be considered the slope m of our equation.
y= mx+ b ⇒
y= 5x - 30
b
To graph our equation we should plot our y-intercept and use our slope to find a second point.
We can then draw a line through those points to show our function.
We already found the y-intercept to be -30 in Part A. Using our graph, we can see that the x-intercept is 6. This means that after the 6^\text{th} groomed pet we will finally break even from our purchase of supplies and we will start making a profit.
