Schaum's Outline of Theory and Problems of Beginning Calculus

CHAP. 41STRAIGHT LINES35DAY+ Y 4YCDCA B x- - + + +A B x A B X(61Fig. 4-164.26 Describe geometrically the families of the following lines, where m and b are any real numbers:(a) y=mx+2(b) y=3x+b4.27 The x-intercept of a line 9 is defined to be the x-coordinate of the unique point where 9 intersects thex-axis. Thus, it is the number U for which (a, 0) lies on 9.(a) Which lines do not have x-intercepts?(b) Find the x-intercepts of (i) 2x - 3y = 4, (ii) x + 7y = 14, (iii) 5x - 13y = 1, (io) x = 3, (U) y = 1.(c) If a and b are the x-intercept and y-intercept of a line, show thatis an equation of the line.X Y-+-=Ia b(d) If (2) is an equation of a line, show that a is the x-intercept and b is the y-intercept.4.28 In the triangle with vertices 43, l), B(2, 7), and C(4, 10) find the slope-intercept equation of: (a) thealtitude from A to side BC; (b) the median from B to side AC; (c) the perpendicular bisector of side AB.