Find the perpendicular and parallel lines using the points

Question

Consider the line

Find the equation of the line that is perpendicular to this line and passes through the point (7,  -6)

Find the equation of the line that is parallel to this line and passes through the point (7,  -6)

[ I keep getting these wrong, but I really need to finish these questions. In order to finish, I need to get three correct consecutively. Please help :( ]

Answer 1

Best to convert the given equation to the slope-intercept form in order to find the slope. y = mx + b, where m is the slope.

-x - 7y = 4. Add x to both sides and divide by -7. y = -x/7 - 4/7, so the slope is -1/7. The perpendicular line has a slope that is the negative reciprocal of -1/7, or 7.

For the perpendicular line through (7, -6), substitute the x and y values into the slope-intercept form to find the intercept. -6 = 7(7) + b -> -6 = 49 + b, b= -55. Equation of perpendicular line is y = 7x - 55.

Do the same with the parallel equation: -6 = (-1/7)7 + b, etc.

Answer 2

The slope of the given lines is -1/7.

The slope of the normal (perpendicular) is 7.

The slope of the parallel line through (7,-6) is

-1/7= (y+6)/(x-7)

This equation can be "massaged" around into whatever form is required.

I will leave the equation of the normal line for you to finish using what I have supplied as an example.