Answer:
Slope is the charge per hour, y-intercept is the flat fee earned by Nicole and the equation to find the cost per hour is [tex]C=m(h)+3[/tex]
For [tex]5[/tex] hours of babysitting amount earned is [tex]28\$[/tex].
Step-by-step explanation:
From the given data lets assign time on x-axis and the amount earned on y-axis.
We have to choose two points.
[tex](x_1,y_1)=(3,18)[/tex] and [tex](x,y)=(5,28)[/tex]
By applying point slope form we have to find the slope of the points.
Slope (m) [tex]= \frac{y-y_1}{x-x_1} =\frac{28-18}{5-3} =\frac{10}{2} =5[/tex]
Here slope is representing per hour charge of Nicole for babysitting.
Now lets find the y-intercept value by plugging the values of [tex](x,y)[/tex] in standard equation of line that is [tex]y=mx+b[/tex] ,equivalent to [tex]C=m(h)+b[/tex] where [tex]b\\[/tex] is the y-intercept.
The equation for cost (C), [tex]C=m(h)+3[/tex] , [tex]h[/tex] is the number of hours.
[tex]b=C-m(h), b=28-5(5), b=28-25=3[/tex]
This y-intercept [tex](b=3)[/tex] is representing the flat fee Nicole will charge for babysitting.
Now
For [tex]5[/tex] hours cost we will put [tex]h=5[/tex] in the equation of cost.
[tex]C=5h+3,C=5(5)+3=28\$[/tex]
For [tex]5[/tex] hours of baby sitting Nicole will earn an amount of [tex]C=5(5)+3=28\$[/tex]
So our final answers are equation of cost [tex]=C=m(h)+3[/tex], y-intercept is the flat fee and slope is the charge per hour.For [tex]5[/tex] hours amount earned is [tex]28\$[/tex].
