Question

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 .

Answer 1

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).

Answer 2

First Blank: 1/2

Second Blank: (0,4)

Third Blank: -2

Fourth Blank: (-2,-2)