Exercise 16 Page 438

The given graph shows the cost of copy paper at two different stores.

In order to construct a linear system, we will write an equation for each line in slope-intercept form. y= mx+ b In this form, m is the slope and b is the y-intercept. First, let's find the slope by using the Slope Formula. m=y_2-y_1/x_2-x_1 Here, (x_1,y_1) and (x_2,y_2) represent the points that are on the line.

Equation for f(x)

Let's start with y=f(x) where x represents the weight. Since the line passes through the points (0,60) and (400,120), we will substitute them into the formula.

Thus, the slope for the line is 0.15. f(x)=0.15x+ b Next, we will determine the y-intercept. Since the line passes through the point (0,60), we can immediately determine the y-intercept is 60. Thus, we can write the equation as the following. f(x)=0.15x+60

Equation for g(x)

Next, we will write an equation for y=g(x) in the same way. Since the line passes through the points (100,39) and (450,161.5), we will substitute them into the formula.

Thus, the slope for this line is 0.35. g(x)=0.35x+ b Now, we will find the y-intercept. Since the line passes through the point (100,39), let's substitute it into g(x) and solve it for b.

We have found the y-intercept as b=4. Thus, the function can be written as the following. g(x)=0.35x+4

System of Equations and Verification

Finally, we have the system of equations. f(x)=0.15x+60 & (I) g(x)=0.35x+4 & (II) In order to determine the amount of copy paper which the cost is the same at both stores, we will setup an equation that f(x) is equal to g(x). f(x)&=g(x) 0.15x+60&=0.35x+4 Let's solve the equation for x.

The amount of copy paper which the cost is the same at both store is 280 lb. In order to verify our answer, lets check the intersection point of two line whether its x-coordinate is 280.

Since the x coordinate of the intersection point is 280, our solution is correct.