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 .

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)