Answer:
a. The slope of a line parallel to the given line is 1
b. A point on the line parallel to the given line, passing through (−4, 2), is (1,7)
c. The slope of the line perpendicular to the given line is -1
d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)
Step-by-step explanation:
The equation of the line in Slope-intercept form is:

Where m is the slope and b is the y-intercept.
a. For the line 
You can identify that:

By definition, two lines are parallel if they have the same slope. Then, the slope of a line parallel to the given line is:

b. The equation of the line in Point-slope form is:

Where m is the slope and (
) is a point of the line.
Given the point (-4,2), substitute this point and the slope of the line into the equation:

Give a value to "x", substitute it into this equation and solve for "y":
For
:



Then, you get the point (1,7)
c. The slopes of perpendicular lines are negative reciprocals, then the slope of a line perpendicular to the given line is:

d. Given the point (-4,2), substitute this point and the slope of the line into the equation:


Give a value to "x", substitute it into this equation and solve for "y":
For
:



Then, you get the point (3,-5)