SOLUTION: Consider the line with the equation: y=(6/5)x−4 Give the equation of the line parallel to Line 1 which passes through (−9,4) : Give the equation of the line perpendic

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Question 1132261: Consider the line with the equation: y=(6/5)x−4
Give the equation of the line parallel to Line 1 which passes through (−9,4) :
Give the equation of the line perpendicular to Line 1 which passes through (−9,4) :
Found 3 solutions by MathLover1, ikleyn, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the line with the equation: y=%286%2F5%29x-4+
Give the equation of the line parallel to Line 1 which passes through (-9,4) :
the line parallel to Line 1 will have same slope, and it is m=%286%2F5%29
since given point, use point slope formula to find equation:
y-y%5B1%5D=m%28x-x%5B1%5D%29...plug in slope and x and y coordinates of the point (-9,4)
y-4=%286%2F5%29%28x-%28-9%29%29
y-4=%286%2F5%29x%2B9
y=%286%2F5%29x%2B%286%2F5%299%2B4
y=%286%2F5%29x%2B54%2F5%2B20%2F5
y=%286%2F5%29x%2B74%2F5



Give the equation of the line perpendicular to Line 1 which passes through (-9,4) :
the line perpendicular to Line 1 will have a slope negative reciprocal to slope o the line 1
m%5Bp%5D=-1%2Fm=>m%5Bp%5D=-1%2F%286%2F5%29=>m%5Bp%5D=-5%2F6
then
y-4=%28-5%2F6%29%28x-%28-9%29%29
y-4=%28-5%2F6%29%28x%2B9%29
y-4=%28-5%2F6%29x-%285%2F6%299
y=%28-5%2F6%29x-45%2F6%2B4
y=%28-5%2F6%29x-45%2F6%2B24%2F6
y=%28-5%2F6%29x-21%2F6
y=%28-5%2F6%29x-7%2F2




Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

It is very elementary and basic skill that every student must develop to the level sufficient to solve such problems on his  (or her)
own without asking assistance from outside.

To help you to develop such skills,  special lessons were created in this site

    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point

Read them and find there the complete explanation on how to do it.

From these lessons,  learn the subject once and for all.


There are accompanied, closely related lessons
    - Find the slope of a straight line in a coordinate plane passing through two given points
    - Equation for a straight line having a given slope and passing through a given point
    - Solving problems related to the slope of a straight line
    - Equation for a straight line in a coordinate plane passing through two given points

Consider all these lessons as your textbook,  handbook and/or a home teacher.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The given line is y = (6/5)x-4; its slope is (6/5).

Parallel lines have the same slopes; perpendicular lines have slopes that are negative reciprocals.

(a) Every line parallel to the given line has an equation of the general form y = (6/5)x+b.

To find the equation of the line parallel to the given line through (-9,4), substitute x=-9 and y=4 in the general form and solve for b.

(b) Every line perpendicular to the given line has an equation of the general form y = (-5/6)x+b.

To find the equation of the line perpendicular to the given line through (-9,4), substitute x=-9 and y=4 in the general form and solve for b.