SOLUTION: write an equation of a line that is parallel to the line 3y-6x=1 and that passes through point (-1,4)

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Question 398673: write an equation of a line that is parallel to the line 3y-6x=1 and that passes through point (-1,4)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
the line 3y-6x=1 and point (-1,4)
3y-6x=1......write in slope-intercept form
3y=6x%2B1
3y%2F3=6x%2F3%2B1%2F3
y=+2x%2B1%2F3
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 (its from the slope of y=2%2Ax%2B%281%2F3%29 which is also 2). Also since the unknown line goes through (-1,4), 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-4=2%2A%28x%2B1%29 Plug in m=2, x%5B1%5D=-1, and y%5B1%5D=4



y-4=2%2Ax-%282%29%28-1%29 Distribute 2



y-4=2%2Ax%2B2 Multiply



y=2%2Ax%2B2%2B4Add 4 to both sides to isolate y

y=2%2Ax%2B6 Combine like terms

So the equation of the line that is parallel to y=2%2Ax%2B%281%2F3%29 and goes through (-1,4) is y=2%2Ax%2B6


So here are the graphs of the equations y=2%2Ax%2B%281%2F3%29 and y=2%2Ax%2B6



graph of the given equation y=2%2Ax%2B%281%2F3%29 (red) and graph of the line y=2%2Ax%2B6(green) that is parallel to the given graph and goes through (-1,4)