Question

Use the facts that parallel lines have equal slopes and that the slopes of perpendicular lines are negative reciprocals of one another. Find equations for the lines through the point (4, 4) that are parallel to and perpendicular to the line with equation y+4x=10 .

Answer 1

For parallel line

y = -4x + 20

For perpendicular line

4y = x + 12

Explanation:

Equations parallel to y + 4x = 10

y = 10 - 4x

Compared to y= mx + c

The slope here is -4.

A line parallel to this particular line will have same slope.

Thus, the slope of the line parallel to that line is also -4.

Now going to the equation of line using the points, we use the following formula

y-y1/x -x1 = m

This means y-4/x-4 = -4

y -4 = -4x + 16

y = -4x + 20

For a line perpendicular to that line, the product of their slope equals -1. Since the slope of the first is -4, then the slope of the perpendicular line would be -1/-4 = 1/4

The equation of the line is thus as used before,

y -y1/x-x1 = m

y - 4/x -4 = 1/4

4y -16 = x -4

4y = x + 12