SOLUTION: Write the equation of the line L satisfying the given geometric conditions. L has y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1

Algebra ->  Equations -> SOLUTION: Write the equation of the line L satisfying the given geometric conditions. L has y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1       Log On


   

Question 100730: Write the equation of the line L satisfying the given geometric conditions.
L has y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1
Found 3 solutions by checkley71, stanbon, jim_thompson5910:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
Y=mX+b
Y=2X/3-3 IS THE EQUATION WITH A SLOPE OF 2/3 & A Y INTERCEPT OF -3.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write the equation of the line L satisfying the given geometric conditions.
L has y-intercept (0,-3) and is parallel to the line with equation y=2/3x+1
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If it is parallel to y = (2/3)x+1, its slope is (2/3)
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So the equation is y = (2/3)x - 3
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Cheers,
Stan H.

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%2B1 which is also 2%2F3). Also since the unknown line goes through (0,-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%2B3=%282%2F3%29%2A%28x-0%29 Plug in m=2%2F3, x%5B1%5D=0, and y%5B1%5D=-3



y%2B3=%282%2F3%29%2Ax-%282%2F3%29%280%29 Distribute 2%2F3



y%2B3=%282%2F3%29%2Ax-0%2F3 Multiply



y=%282%2F3%29%2Ax-0%2F3-3Subtract -3 from both sides to isolate y

y=%282%2F3%29%2Ax-0%2F3-9%2F3 Make into equivalent fractions with equal denominators



y=%282%2F3%29%2Ax-9%2F3 Combine the fractions



y=%282%2F3%29%2Ax-3 Reduce any fractions

So the equation of the line that is parallel to y=%282%2F3%29%2Ax%2B1 and goes through (0,-3) is y=%282%2F3%29%2Ax-3


So here are the graphs of the equations y=%282%2F3%29%2Ax%2B1 and y=%282%2F3%29%2Ax-3



graph of the given equation y=%282%2F3%29%2Ax%2B1 (red) and graph of the line y=%282%2F3%29%2Ax-3(green) that is parallel to the given graph and goes through (0,-3)