126,076 views
1 vote
1 vote
Write an equation of the line through (2,5) and parallel to y=3x-8. Write the Equation in the form x=a, y=b, or Y=MZ+b

User Troy Gizzi
by
2.7k points

1 Answer

11 votes
11 votes

The equation of the given line is

y = mx + c

where

m = slope

c = y intercept

The equation of the given line is

y = 3x - 8

By comparing both equations,

m = 3

Recall, if two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. The negative reciprocal of 3 is - 1/3. Thus, the slope of the perpendicular line passing through (2, 5) is - 1/3

We would fnd the y intercept, c by substituting m = - 1/3, x = 2 and y = 5 into the slope intercept equation. We have

5 = - 1/3 * 2 + c = - 2/3 + c

c = 5 + 2/3 = 17/3

Thus, the equation of the perpendicular line is

y = - x/3 + 17/3

User Yoh Deadfall
by
3.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.