consider the line y=-7x+7

Question

consider the line y=-7x+7
Find the equation of the line that is parallel to this line and passes through the point (2, 5)
Find the equation of the line that is perpendicular to this line and passes through the point (2, 5)

Answer 1

Hello Berenice,

 

The following is a breakdown to the solution of your math problem:

 

English: parallel lines have same slope but different y-intercepts, therefore identify slope of given equation.

Math:

y = -7x + 7 ---> slope = -7

 

English: Identify and label given point (2,5)

Math:

x = 2, y =5

 

English: write slope intercept format and substitute and solve for b (the y-intercept)

Math:

y = mx + b

m = -7 , x = 2, y = 5

 

5 = (-7)(2) + b

5 = -14 + b                     (add 14 to both sides)

5 + 14 = -14 + 14

19 = b

 

English: Rewrite equation of parallel line that passes through point (2,5)

Math:

y = -7x + 19

 

English: Identify perpendicular lines slope which is the negative reciprocal of given linear equation

Math:

given slope = -7 ---> perpendicular slope is 1/7

 

English: identify and label given point of perpendicular line

Math:

point (2,5) ---> x = 2, and y = 5

 

English: Write slope intercept format and substitute and solve for b

Math:

y = mx + b ---> m = 1/7, x = 2, and y = 5

5 = (1/7)(2) + b

5 = 2/7 + b      (subtract 2/7 from each side)

5 - 2/7 = 2/7 - 2/7 + b

33/7 = b

 

English: rewrite equation of perpendicular line

Math:

y = 1/7x + 33/7

 

I hope that helps. Let me know if you have any questions.

 

 

 

Answer 2

equation of a line parallel

 

slope is m=-7

(2,5)

 

y-y1=m(x-x1)

y-5=-7(x-2)

y-5=-7x+14

y=-7x+19

 

equation of line that is perpendicular 

slope is equal to negative reciprocal of slope

m=- 1/-7=1/7

y-5=1/7(x-2)

y-5=1/7x-2/7

y=1/7x+33/7