Algebra Know-It-ALL

332 Review Questions and Answers

and

y= (1/3)x+ 3

We know from these equations that the y-intercepts are 8 and 3, so the point (0, 8) is on

the first line and the point (0, 3) is on the second line. The solution to the system, as we’ve

already determined, is (−3, 2). That point lies on both lines. Figure 20-6 shows plots of

these three points, along with plots of the lines connecting the points and representing the

equations.

Question 17-2

How can we determine the x-intercept of the line representing the equation y= 2 x+ 8 on the

basis of the known slopes and the point data in Fig. 20-6? (We can set y= 0 and then calculate

x by arithmetic, but the purpose of this exercise is to demonstrate the geometric principles of

slope and intercept.)

Answer 17-2

The slope of the line is 2. Therefore, if we start from any point on the line and move in the

positive x direction by n units, we must move in the positive y direction by 2n units to stay on

the line. In the opposite sense, if we start from any point on the line and move in the negative y

direction by p units, we must move in the negative x direction by p/2 units to stay on the line.

Let’s start at the point (0, 8), which is the y-intercept. If we move in the negative y direction

y= (1/3)x+ 3

y= 2x+ 8

(0,8)

(0,3)

Each axis

increment

is 1 unit

Solution =

(–3,2)

x

y

Figure 20-6 Illustration for Questions and Answers

17-1 through 17-6.