Coach pug will train your dog for a membership fee of 45 dollar and a session fee of 20 dollars. Dr. Doberman will train your dog for no membership fee, but a session fee of 30 dollars per session.

Coach pug charges $45 only one time, and an additional of $20 per session.

So if you take x sessions, the total cost will be:

c(x) = $45 + $20*x

Dr. Doberman charges only $30 per session, then the cost for x sessions will be_

d(x) = $30*x

Now, which one is better for you?

We need to see the value of x such that:

d(x) = c(x)

$30*x = $45 + $20*x

$30*x - $20*x = $45

$10*x = $45

x = $45/$10 = 4.5

This means that if you take 4 sessions or less, is better the Dr. Doberman, because in this case we do not have an y-intercept.

If you want to have 5 sessions or more, is better Coach Pug, because the slope of the equation is smaller, so the costs for larger values of x will be smaller.

this doesn't make sense lol