Question

Most plumbing companies charge a fee to come to your house plus a charge per hour of work. The fees and charges for two plumbing companies are shown.
Company A Fee: $50 Charge per hour: $40 Company B Fee: $25 Charge per hour: $50

Write an equation for each company, where c = total cost (in dollars) and h = number of hours. Explain what the initial values and rates of change mean in this context.

Company A: Company B:​

Answer 1

Answer:

Company A: $y=40x+50$

Company B: $y=50x+25$

Step-by-step explanation:

The initial fee is the y-intercept, as that is the cost at x = 0, or the cost before any time has passed. Afterwards, the rate the cost increases is the slope.

Linear equation in slope-intercept form:

$y=mx+b$

where m is the slope and b is the y-intercept.

Company A charges $50 up front and $40 per hour afterwards, so the equation would be:

$y=40x+50$

Company B charges $25 up front and $50 per hour, so:

$y=50x+25$