SOLUTION: Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,9) and perpendicular to 2x+7y=1.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,9) and perpendicular to 2x+7y=1.      Log On


   

Question 978001: Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (1,9) and perpendicular to 2x+7y=1.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

line passing through (1,9) and perpendicular to 2x%2B7y=1
in slope-intercept form:
7y=-2x%2B1
y=-%282%2F7%29x%2B1%2F7
Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line


Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of 2%2F7, you can find the perpendicular slope by this formula:

m%5Bp%5D=-1%2Fm where m%5Bp%5D is the perpendicular slope


m%5Bp%5D=-1%2F%282%2F7%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%287%2F2%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-7%2F2 Multiply the fractions.


So the perpendicular slope is -7%2F2



So now we know the slope of the unknown line is -7%2F2 (its the negative reciprocal of 2%2F7 from the line y=%282%2F7%29%2Ax%2B1%2F7). Also since the unknown line goes through (1,9), 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-9=%28-7%2F2%29%2A%28x-1%29 Plug in m=-7%2F2, x%5B1%5D=1, and y%5B1%5D=9



y-9=%28-7%2F2%29%2Ax%2B%287%2F2%29%281%29 Distribute -7%2F2



y-9=%28-7%2F2%29%2Ax%2B7%2F2 Multiply



y=%28-7%2F2%29%2Ax%2B7%2F2%2B9Add 9 to both sides to isolate y

y=%28-7%2F2%29%2Ax%2B7%2F2%2B18%2F2 Make into equivalent fractions with equal denominators



y=%28-7%2F2%29%2Ax%2B25%2F2 Combine the fractions



y=%28-7%2F2%29%2Ax%2B25%2F2 Reduce any fractions

So the equation of the line that is perpendicular to y=%282%2F7%29%2Ax%2B1%2F7 and goes through (1,9) is y=%28-7%2F2%29%2Ax%2B25%2F2


So here are the graphs of the equations y=%282%2F7%29%2Ax%2B1%2F7 and y=%28-7%2F2%29%2Ax%2B25%2F2




graph of the given equation y=%282%2F7%29%2Ax%2B1%2F7 (red) and graph of the line y=%28-7%2F2%29%2Ax%2B25%2F2(green) that is perpendicular to the given graph and goes through (1,9)