Question

Consider the line y = 6x - 6. Find the equation of the line that is perpendicular to this line and passes through the point (-4, -5). Find the equation of the line that is parallel to this line and passes through the point (-4, -5).

A) Perpendicular line: y = -1/6x - 1, Parallel line: y = 6x + 21
B) Perpendicular line: y = -6x + 21, Parallel line: y = 6x - 21
C) Perpendicular line: y = -6x - 5, Parallel line: y = 6x + 5
D) Perpendicular line: y = 6x + 5, Parallel line: y = -6x - 5

Answer 1

To find the equation of a line that is perpendicular to the given line and passes through a given point, determine the slope of the given line and find the negative reciprocal. For the line parallel to the given line, use the same method without the negative reciprocal. The given equations are correct A) Perpendicular line: y = -1/6x - 1, Parallel line: y = 6x + 21

Step-by-step explanation:

To find the equation of a line that is perpendicular to the given line and passes through a given point, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The negative reciprocal will be the slope of the perpendicular line.

Using the equation y = mx + b, where m is the slope and b is the y-intercept, we can substitute the point (-4, -5) to find the y-intercept of the perpendicular line. Once we have the slope and y-intercept, we can write the equation of the perpendicular line in the form y = mx + b.

For the line that is parallel to the given line and passes through the same point, we can use the same method but without taking the negative reciprocal of the slope. The equation will be in the form y = mx + b.

The correct answers are:

Perpendicular line: y = -1/6x - 1

Parallel line: y = 6x + 21