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Question 583549: Find (a) the equation of a line that is parallel to the given line and includes the given point, and (b) the equation of a line that is perpendicular to the given line through the given point. Write both answers in slope-intercept form. (c) Graph both of these lines on the same axes Please show all of your work.
y = -4x + 2, (5, 4)
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! PARALLEL
4 x + y = 2
Find the slope of this line
make y the subject
y = -4 x + 2
Compare this equation with y=mx+b
slope m = -4
The slope of a line parallel to the above line will be the same
The slope of the required line will be -4
m= -4 ,point ( 5 , 4 )
Find b by plugging the values of m & the point in
y=mx+b
4 = -20 + b
b= 24
m= -4
Plug value of the slope and b in y = mx +b
The required equation is y=-4x +24
PERPENDICULAR
4 x + y = 2
Find the slope of this line
y = -4 x + 2
Compare this equation with y=mx+b,
m= slope & b= y intercept
slope m = -4
The slope of a line perpendicular to the above line will be the negative reciprocal= 1/4
m1*m2=-1
m= 1/4 ,point ( 5 , 4 )
Find b by plugging the values of m & the point in
y=mx+b
4 = 5/ 4 + b
b= 11/4
m= 1/4
The required equation is y = 1/ 4 x+11/ 4
m.ananth@hotmail.ca
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