SOLUTION: The equation of line q is 5y - 4x = 10. Write the standard form of the equation of the line that fits the following description: parallel to q and passes through the point at (

Algebra ->  Linear-equations -> SOLUTION: The equation of line q is 5y - 4x = 10. Write the standard form of the equation of the line that fits the following description: parallel to q and passes through the point at (      Log On


   

Question 918917: The equation of line q is 5y - 4x = 10. Write the standard form of the equation of the line that fits the following description:
parallel to q and passes through the point at (-15, 8)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of line q is
5y+-+4x+=+10
5y+=4x+%2B+10
y+=%284%2F5%29x+%2B+10%2F5
y+=%284%2F5%29x+%2B+2
find: the line parallel to q and passes through the point at (-15,+8)
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 4%2F5 (its from the slope of y=%284%2F5%29%2Ax%2B2 which is also 4%2F5). Also since the unknown line goes through (-15,8), 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-8=%284%2F5%29%2A%28x%2B15%29 Plug in m=4%2F5, x%5B1%5D=-15, and y%5B1%5D=8



y-8=%284%2F5%29%2Ax-%284%2F5%29%28-15%29 Distribute 4%2F5



y-8=%284%2F5%29%2Ax%2B60%2F5 Multiply



y=%284%2F5%29%2Ax%2B60%2F5%2B8Add 8 to both sides to isolate y

y=%284%2F5%29%2Ax%2B60%2F5%2B40%2F5 Make into equivalent fractions with equal denominators



y=%284%2F5%29%2Ax%2B100%2F5 Combine the fractions



y=%284%2F5%29%2Ax%2B20 Reduce any fractions

So the equation of the line that is parallel to y=%284%2F5%29%2Ax%2B2 and goes through (-15,8) is y=%284%2F5%29%2Ax%2B20


So here are the graphs of the equations y=%284%2F5%29%2Ax%2B2 and y=%284%2F5%29%2Ax%2B20



graph of the given equation y=%284%2F5%29%2Ax%2B2 (red) and graph of the line y=%284%2F5%29%2Ax%2B20(green) that is parallel to the given graph and goes through (-15,8)