for babysitting nicole charges a flat fee of 3$ plus 5$ per hour.write a linear function. how much money will she make if she baby-sits 5 hours?

Question

what is the y=mx+b of this and the function notation and the answer to the question? thx

Answer 1

For the linear equation y = mx + b, m is the slope (the change in y for a change in x) and b is the y intercept, i.e. the value of y when x is zero.  For this problem, b (y-intercept) is the money Nicole would make even if the hours she babysits was zero, i.e. the flat fee.  Therefore, b = $3.  The slope m is the money she makes babysitting per hour, i.e. $5.  Therefore, the equation is

 

     y = 5*x + 3. 

 

In function notation we just replace y with f(x) (meaning the output of the function f for input x):

 

     f(x) = 5*x + 3.

 

In five hours (x = 5), Nicole would make:

 

     y = 5*5 + 3 = 25 + 3 = $28.