What is the equation of the line parallel to the graph of #4x+3y=9# that passes through the point #(2, -1)#?

1 Answer
Mia
Apr 24, 2017

#y_1=(-4/3)x+5/3#

Explanation:

Two straight lines are parallel if and only if they have same slope.
#" "#
Name the new straight line parallel to the given straight line is
#" "#
#y_1=a_1x+b_1#
#" "#
#4x+3y=9#
#" "#
#rArr3y=-4x+9#
#" "#
#rArry=(-4/3)x+9/3#
#" "#
#rArry=(-4/3)x+3#
#" "#
The slope in the given straight line is #-4/3# then the #a_1=-4/3#
#" "#
Since the straight line#" "color(blue)(y_1)" "#passes through the
#" "#
point #(2,-1)# we can easily find #color(blue)(b_1)#
#" "#
#-1=-4/3(2)+b_1#
#" "#
#rArr-1=-8/3+b_1#
#" "#
#rArrb_1=-1+8/3#
#" "#
#rArrb_1=+5/3#
#" "#
Therefore, the equation of the straight line is :
#" "#
#y_1=(-4/3)x+5/3#

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