How do you draw the line that is parallel to #y=-1/2x+5# and passes through the point (2, -3)?

1 Answer
hev1
Mar 26, 2018

The equation of the line parallel to #y = -1/2x+5# that passes through the point #(2, -3)# is #y = -1/2x-2#.

Explanation:

The slope of the line parallel to another line is the same as that of the other line. Therefore, the slope of the line parallel to #y=-1/2x+5# is #-1/2# because the slope of that line is #-1/2#.

Using point-slope form, #y - y_1 = m(x-x_1)# where #y-1# and #x_1# are points from a given coordinate pair #(x,y)# that lies on the line, and #m# is the slope.

Plugging in #-1/2# for #m#, #2# for #x_1#, and #-3# for #y_1#:
#y-(-3) = -1/2(x-2)#
#y + 3 = -1/2x + 1#
#y = -1/2x -2#

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