What is the equation of the line which is parallel to #y = 2x-9# and which passes through the point #(4,2)#?

1 Answer
Jennifer G. · 256 · EZ as pi
Jan 8, 2018

#y=2x-6#

Explanation:

The original formula for the slope is given in the form of

#y=mx+b#,

where #m# is the slope and #b# is the place where the line intersects the y axis, or "#y#-intercept".

In a parallel line, the slope is the same, but the #y#-intercept is different. So, your #m# value remains the same, #(m=2)# but you pick a different #b# value.

In order to choose the appropriate #b# value for the equation of the line we want, we will need to find a line with the same slope that passes through the point #(4,2)# which is #(x,y)#

So, with #m=2#, set #y=2# and #x=4#, and notice that we get #2=2(4)+b#.

Then we have #2=8+b#, which means the choice of #b# we want is #b=-6#.

This gives us the parallel line #y=2x-6#.

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