Randolph runs a home appliance repair business and charges a service call fee of $85 plus $15 per half hour for his labour. Write an equation for calculating the total charges, C, in terms of hours of labour, H. Plot the graph of C vs. H and define the slope and C-intercept of the line.

C=85+15H

To write an equation for calculating the total charges in terms of hours of labor, we first need to determine the relationship between the total charges (C) and the hours of labor (H).

According to the information provided, Randolph charges a service call fee of $85 plus $15 per half hour of labor. This means that for each half hour of labor, Randolph charges an additional $15.

To calculate the total charges, we can start with the service call fee of $85 and add the charges for each half hour of labor. Since each half hour of labor adds $15, the number of half hours of labor can be represented as (2 * H) since there are 2 half hours in an hour.

Therefore, the equation for calculating the total charges, C, in terms of hours of labor, H, is:

C = 85 + 15 * (2 * H)

Simplifying this equation, we have:

C = 85 + 30H

Now, let's plot the graph of C vs. H:

On the y-axis, we have the total charges (C), and on the x-axis, we have the hours of labor (H).

The slope of the line represents the rate at which the charges increase with each additional hour of labor. In this case, the slope is 30, which means that for every additional hour of labor, the charges increase by $30.

The y-intercept of the line represents the total charges when there are zero hours of labor, which is the service call fee of $85. So, the y-intercept or C-intercept is 85.

The graph of C vs. H will be a straight line with a slope of 30 passing through the y-intercept of 85.

Please note that the graph may differ depending on the range of hours of labor you choose to plot.