What is the equation for a line that passes through W(2, -3) and is parallel to the line y=3x +5?

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Doing a math review, stuck on some of these.

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Answer 1 · 2018-06-11T00:14:34

#"y = 3x - 9#

Given: #W(2, -3)# and the line #y = 3x + 5#

Parallel lines have the same slope. Find the slope of the given line. A line in the form of #y = mx + b# reveals the slope.

From the given line, #m = 3#

One way to find the parallel line through #(2, -3)# is to use the point-slope form of a line, #" "y - y_1 = m(x - x_1)#:

#y - -3 = 3 (x - 2)#

#y + 3 = 3x - 6#

Subtract the #3# from both sides: #" "y = 3x - 6 - 3#

Simplify: #" "y = 3x - 9#

A second way is to use #y = mx + b# and use the point #(2, -3)# to find the #y#-intercept #(0, b)#:

#-3 = 3(2) +b#

#-3 = 6 + b#

#-3 -6 = b#

#b = -9#

#y = 3x - 9#