a For the situation in Figure 515 prove that the slope betwe

a. For the situation in Figure 5.15, prove that the slope between points A1 and B1 equals the slope between A2 and B2.

b. Prove that the slope of a horizontal line is zero.

4. a. For the situation in Figure 5.15, prove that the slope between points Ai and Bi equals the slope between A2 and B2. b. Prove that the slope of a horizontal line is zero. 2 B2 FIGURE 5.15 Figure for Exercise 4

Solution

(a) Let the slope of the line A1B1 = m1 and the slope of the line A2B2 = m2

Since all 4 points lie on the same line, hence the equation of both lines will be the same,

y = m1x + c is equal to y = m2x + c, where c is the y intercept, the point where the line cuts the y axis)

Equating we get m1x + c = m2x + c

cancelling c from both sides we get m1x = m2x

Therefore m1 = m2

(b) For any number of points on a horizontal line(a line parallel to the x axis) the value of y will always remain the same. Hence any 2 points on a horozontal line can be taken as A(x1,y) and B(x2,y).

The slope (m) of a line is given by the equation m = (y2-y1)/(x2-x1), but since y2 = y1 = y,

Therefore m = (y - y)/(x2-x1) = 0