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.

Algebra ->  Linear-equations -> 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.       Log On


   

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) About Me  (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 2%2F3 (its from the slope of y=%282%2F3%29%2Ax%2B6 which is also 2%2F3). 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:

y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope and (x%5B1%5D,y%5B1%5D) is the given point



y%2B2=%282%2F3%29%2A%28x-4%29 Plug in m=2%2F3, x%5B1%5D=4, and y%5B1%5D=-2



y%2B2=%282%2F3%29%2Ax-%282%2F3%29%284%29 Distribute 2%2F3



y%2B2=%282%2F3%29%2Ax-8%2F3 Multiply



y=%282%2F3%29%2Ax-8%2F3-2Subtract -2 from both sides to isolate y

y=%282%2F3%29%2Ax-8%2F3-6%2F3 Make into equivalent fractions with equal denominators



y=%282%2F3%29%2Ax-14%2F3 Combine the fractions



y=%282%2F3%29%2Ax-14%2F3 Reduce any fractions

So the equation of the line that is parallel to y=%282%2F3%29%2Ax%2B6 and goes through (4,-2) is y=%282%2F3%29%2Ax-14%2F3


So here are the graphs of the equations y=%282%2F3%29%2Ax%2B6 and y=%282%2F3%29%2Ax-14%2F3



graph of the given equation y=%282%2F3%29%2Ax%2B6 (red) and graph of the line y=%282%2F3%29%2Ax-14%2F3(green) that is parallel to the given graph and goes through (4,-2)





So the answer is C