SOLUTION: Please help with this problem: Which of the following equations is parallel to y =(2/3)x + 6 and contains the point (4, -2)? a. y = (2/3)x + 14 b. y = 3x - 3 c.

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Question 90994: Please help with this problem:
Which of the following equations is parallel to y =(2/3)x + 6 and contains the
point (4, -2)?
a. y = (2/3)x + 14
b. y = 3x - 3
c. y = (2/3)x - (14/3)
I know it has to be a. or c. because the slopes are the same as the question, but I can't figure out how to do the rest. Thank you for your help.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ). Also since the unknown line goes through (4,-2), we can find the equation by plugging in this info into the point-slope formula

Point-Slope Formula:

where m is the slope and (,) is the given point



Plug in , , and



Distribute



Multiply



Subtract from both sides to isolate y

Make into equivalent fractions with equal denominators



Combine the fractions



Reduce any fractions

So the equation of the line that is parallel to and goes through (,) is


So here are the graphs of the equations and



graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)





So the answer is C
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