How many months corresponds to the cost of the installation fee?
A
Example Equation: y-214.70=29.95(x-6)
B
$ 35, see solution.
Practice makes perfect
We want to write an equation for the total cost we pay for cable television after x months. Let's name the total cost y. We want the equation to be in point-slope form, where m is the slope and (x_1,y_1) is one point that the line passes through.
y-y_1=m(x-x_1)
The slope m represents the change in y that corresponds to the change in x. In our case, the cost increases by $ 29.95 per month. This means that m= 29.95.
y-y_1= 29.95(x-x_1)
We are also given that the cost is $ 214.70 after 6 months. This means that the line passes through the point ( 6, 214.70). We can substitute 6 for x_1 and 214.70 for y_1 to get our equation. Let's do it!
y- 214.70=29.95(x- 6)
Please note that any point on the line can be used in place of (x_1,y_1) so there are many correct equations for this line, ours is just one possible answer. To find other possible answers, we could have either graphed the equation or solved for different points on the line.
We want to determine how much the installation fee for cable television is. In Part A we found an equation for the total cost y after x months.
y-214.70=29.95(x-6)The installation fee corresponds to the cost after 0 months. Therefore, we can substitute 0 for x in our equation to find the installation fee.
