SOLUTION: Parallel to y=1/3x+4 and passes through the point (-2,3)

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Question 1021286: Parallel to y=1/3x+4 and passes through the point (-2,3)
Answer by MathLover1(20850) 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 1%2F3 (its from the slope of y=%281%2F3%29%2Ax%2B4 which is also 1%2F3). Also since the unknown line goes through (-2,3), 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-3=%281%2F3%29%2A%28x%2B2%29 Plug in m=1%2F3, x%5B1%5D=-2, and y%5B1%5D=3



y-3=%281%2F3%29%2Ax-%281%2F3%29%28-2%29 Distribute 1%2F3



y-3=%281%2F3%29%2Ax%2B2%2F3 Multiply



y=%281%2F3%29%2Ax%2B2%2F3%2B3Add 3 to both sides to isolate y

y=%281%2F3%29%2Ax%2B2%2F3%2B9%2F3 Make into equivalent fractions with equal denominators



y=%281%2F3%29%2Ax%2B11%2F3 Combine the fractions



y=%281%2F3%29%2Ax%2B11%2F3 Reduce any fractions

So the equation of the line that is parallel to y=%281%2F3%29%2Ax%2B4 and goes through (-2,3) is y=%281%2F3%29%2Ax%2B11%2F3


So here are the graphs of the equations y=%281%2F3%29%2Ax%2B4 and y=%281%2F3%29%2Ax%2B11%2F3



graph of the given equation y=%281%2F3%29%2Ax%2B4 (red) and graph of the line y=%281%2F3%29%2Ax%2B11%2F3(green) that is parallel to the given graph and goes through (-2,3)