Consider the line y = 7x - 6.

Find the equation of the line that is perpendicular to this line and passes through the point (-6, 2).
Find the equation of the line that is parallel to this line and passes through the point (-6, 2).
Note that the ALEKS graphing calculator may be helpful in checking your answer.

1 answer

To find the equation of the line that is perpendicular to y = 7x - 6, we first need to find the slope of the original line. The slope of y = 7x - 6 is 7. Since the line we want is perpendicular, the slope of the new line will be the negative reciprocal of 7, which is -1/7.

Using the point-slope form of a linear equation, the equation of the line perpendicular to y = 7x - 6 that passes through the point (-6, 2) is:
y - 2 = (-1/7)(x + 6)

Simplifying this equation, we get:
y - 2 = -1/7x - 6/7
y = -1/7x + 8/7

Therefore, the equation of the line perpendicular to y = 7x - 6 that passes through the point (-6, 2) is y = -1/7x + 8/7.

To find the equation of the line that is parallel to y = 7x - 6, we simply keep the same slope of 7. Using the point-slope form of a linear equation, the equation of the line parallel to y = 7x - 6 that passes through the point (-6, 2) is:
y - 2 = 7(x + 6)

Simplifying this equation, we get:
y - 2 = 7x + 42
y = 7x + 44

Therefore, the equation of the line parallel to y = 7x - 6 that passes through the point (-6, 2) is y = 7x + 44.