SOLUTION: i really need help how do you write an equation of a line that contains the given point and is parrallel to the given line?? (4,1) y=3X-2 please help me

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Question 117630This question is from textbook
: i really need help
how do you write an equation of a line that contains the given point and is parrallel to the given line??
(4,1) y=3X-2
please help me This question is from textbook

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 3 (its from the slope of y=3%2Ax-2 which is also 3). Also since the unknown line goes through (4,1), 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-1=3%2A%28x-4%29 Plug in m=3, x%5B1%5D=4, and y%5B1%5D=1



y-1=3%2Ax-%283%29%284%29 Distribute 3



y-1=3%2Ax-12 Multiply



y=3%2Ax-12%2B1Add 1 to both sides to isolate y

y=3%2Ax-11 Combine like terms

So the equation of the line that is parallel to y=3%2Ax-2 and goes through (4,1) is y=3%2Ax-11


So here are the graphs of the equations y=3%2Ax-2 and y=3%2Ax-11



graph of the given equation y=3%2Ax-2 (red) and graph of the line y=3%2Ax-11(green) that is parallel to the given graph and goes through (4,1)