Question #7356c

2 Answers
Dec 11, 2017

Answer:

#-1/5x-6/5=y#

Explanation:

First, remember that the equation #-1/mx+b=y# is perpendicular to #mx+b=y#

First, write #5x-y=3# in the intercept form #y=mx+b#

#5x-y=3#
#5x=3+y#
#5x-3=y#

Since the slope is 5, the slope for the perpendicular line is #-1/5#

Since this line perpendicular to #5x-3=y# passes through (4,-2), we can use the formula #m(x-x_1)=y-y_1# to find the equation.

#-1/5(x-4)=y-(-2)# We need to make this into the form #y=mx+b#

#-1/5(x-4)=y-(-2)#

#-x/5+4/5=y+2#
#-x/5+4/5-2=y#
#-x/5-6/5=y#
#-1/5x-6/5=y#
That is our answer! To prove this, simply graph these two points.

Desmos

Dec 11, 2017

Answer:

#y+2=-\frac{1}{5}(x-4)#

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other.

So the perpendicular line will have a slope of #-\frac{1}{5}#.

Now we can write the equation in point-slope form:

#y-y_1=m(x-x_1)#

#\implies y+2=-\frac{1}{5}(x-4)#