Exercise 15 Page 437

We have been given a graph that shows the cost of making a movie depending on the film length for two different companies.

We can write an equation for each line in slope-intercept form. y=mt+ b In this form, m is the slope and b is the y-intercept. We will find the slope of the lines by using the Slope Formula. m=y_2-y_1/t_2-t_1 In the above formula, (t_1,y_1) and (t_2,y_2) represent two points of the line.

Equation for f(t)

Let's start with y=f(t), where t represents the number of days. Since the line passes through the points (0,125) and (6,230), we will substitute them into the Slope Formula in order to find the slope.

Thus, the slope of this line is 17.5. f(t)=17.5t+ b Next, we will determine the y-intercept. Since the line passes through the point (0, 125), we can immediately determine the y-intercept as 125. Thus, we can write the full equation of the line. f(t)=17.5t+ 125

Equation for g(t)

We will write an equation for y=g(t) in the same way as we did for f(t). Since the line passes through the points (0,20) and (6,230), we will substitute them into the Slope Formula to find the slope.

Thus, the slope for this line is 35. g(t)=35t+ b Let's find the y-intercept now. Since the line passes through the point (0, 20), we can immediately determine the y-intercept as 20. g(t)=35t+ 20

System of Equations

Finally, we have our system of linear equations. f(t)=17.5t+125 & (I) g(t)=35t+20 & (II) The points (0,125) and (0,20) indicate the initial cost for making a film for each company, $125 and $20. The solution of the system is the point of intersection of the lines, (6,230). It represents the cost of making a 6- minute long film, which is $230.