SOLUTION: parallel to 5x-2y=-3 and passes through Q(-4,0)

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Question 1076570: parallel to 5x-2y=-3 and passes through Q(-4,0)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
parallel to 5x-2y=-3=>2y=5x%2B3=>y=%285%2F2%29x%2B3%2F2
and passes through Q(-4,0)

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 5%2F2 (its from the slope of y=%285%2F2%29%2Ax%2B3%2F2 which is also 5%2F2). Also since the unknown line goes through (-4,0), 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-0=%285%2F2%29%2A%28x%2B4%29 Plug in m=5%2F2, x%5B1%5D=-4, and y%5B1%5D=0



y-0=%285%2F2%29%2Ax-%285%2F2%29%28-4%29 Distribute 5%2F2



y-0=%285%2F2%29%2Ax%2B20%2F2 Multiply



y=%285%2F2%29%2Ax%2B20%2F2%2B0Add 0 to both sides to isolate y

y=%285%2F2%29%2Ax%2B20%2F2%2B0%2F2 Make into equivalent fractions with equal denominators



y=%285%2F2%29%2Ax%2B20%2F2 Combine the fractions



y=%285%2F2%29%2Ax%2B10 Reduce any fractions

So the equation of the line that is parallel to y=%285%2F2%29%2Ax%2B3%2F2 and goes through (-4,0) is y=%285%2F2%29%2Ax%2B10


So here are the graphs of the equations y=%285%2F2%29%2Ax%2B3%2F2 and y=%285%2F2%29%2Ax%2B10



graph of the given equation y=%285%2F2%29%2Ax%2B3%2F2 (red) and graph of the line y=%285%2F2%29%2Ax%2B10(green) that is parallel to the given graph and goes through (-4,0)