Exercise 7 Page 312

We are given a table showing the number of meter y that a water-skier travels in x minutes.

Minutes, x	1	2	3	4	5
Meters, y	600	1200	1800	2400	3000

Functions written in slope-intercept form follow a specific format. y= mx+ b In this form, m is the slope and b is the y-intercept. We need to identify these values using the given table. Let's start by substituting the points (1,600) and (2,1200) into the slope formula and calculating m.

We found that the slope of the given equation is 600. Now we can write a partial function by substituting m= 600. y= 600x+ b Remember that the y-intercept is the y-value where the line crosses the y-axis. To find it, we will use a point of the table in the above equation and solve it for b. Let's use ( 3, 1800).

The function intercepts the y-axis at (0, 0), so the value of b is 0. Now that we have the slope and the y-intercept, we can write a equation for the line that passes through the given points. y= 600x+ 0 → y=600x

We want to graph the linear function we wrote in Part A. y=600x Recall that the points given in the table lie on a line. The value of x and its corresponding value of y represent a ordered pair that can be plotted in a coordinate plane. Let's plot the ordered pairs and draw a line through the points.

We want to find how many kilometers the water-skier will travel in 12 minutes. Let's use the function we wrote in Part A. y=600xRecall that y represents the meters traveled and that x is the number of minutes spent skiing. We can substitute x= 12 to find the meters traveled in 12 minutes.

We found that the water-skier will travel 7200 meters in 12 minutes. However, we want to find the distance in kilometers. Remember that 1000 meters is equal to 1 kilometer. This means that we can divide 7200 by 1000 to convert the distance into kilometers. 7200/1000= 7.2 Therefore, the water-skier will travel 7.2 kilometers in 12 minutes.

We are told that another water-skier travels at the same rate but starts a minute after the first water-skier. This can be represented by a function of the same form of the one obtained in Part A, but this one will have a b=- 1. y=600x -1 Now we can plot the function of each water-skier in the same coordinate plane. Since both skiers travel at the same rate, the linear functions will be parallel lines.

Notice that at any time, the value of the blue line is greater than the value of red line. This means that the second water-skier will always be behind the first water-skier.