Consider the graph of the line y = x – 4 and the point (−4, 2). The slope of a line parallel to the given line is . A point on the line parallel to the given line, passing through (−4, 2), is . The slope of a line perpendicular to the given line is . A point on the line perpendicular to the given line, passing through (−4, 2), is .
Accepted Solution
A:
The given line is y = x - 4, and the given point is (-4, 2).
The slope of the given line is 1, and its y-intercept is (0, -4).
Part a. The slope of a line parallel to the given line is 1.
Part b. Let the equation of a line parallel to the given line be y = x + c Let (x,y) be a point on a parallel line which passes through (-4,2). Then, in point-slope form, (y - 2)/(x + 4) = 1 That is, y - 2 = x + 4 y = x + 6
If x = 0, then y - 2 = 0 + 4 y - 2 = 4 y = 6 Therefore the point (0, 6) is one of many points that lies on this line.
Part c. The slope of a line perpendicular to the given line is -1. The product of the slopes of perpendicular lines is -1.
Let (x,y) be a point on the perpendicular line which passes through (-4,2). In point-slope form, its equation is (y - 2)/(x + 4) = -1 That is, y - 2 = -x - 4 y = -x - 2 Wneh x = 0, then y = -2. A point on the perpendicular line that passes through (-4,2) is (0, -2).
Answers: 1. The slope is 1. 2. The point (0, 6) falls on the parallel line passing through (-4, 2). 3. The slope of a perpendicular line is -1. 4. The point (0, -2) falls on the perpendicular line passing through (-4, 2).