SOLUTION: I want to double check my answer regarding the following math problem: Write an equation in the slope intercept form if possible: for the line which is at (0,-3) and is perpendi

Algebra ->  Graphs -> SOLUTION: I want to double check my answer regarding the following math problem: Write an equation in the slope intercept form if possible: for the line which is at (0,-3) and is perpendi      Log On


   

Question 102629: I want to double check my answer regarding the following math problem:
Write an equation in the slope intercept form if possible: for the line which is at (0,-3) and is perpendicular to x - 2y = 7
My equation is:
x-2y=7
x=2y+7
2y+y=x
2y/2 = x/2 - 7/2
Y intercept is x/2 - 7/2
Now I'm lost as far as the slope is concerned
Please help

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!



First convert the standard equation x-2y=7 into slope intercept form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from standard form (Ax+By = C) to slope-intercept form (y = mx+b)


1x-2y=7 Start with the given equation


1x-2y-1x=7-1x Subtract 1x from both sides


-2y=-1x%2B7 Simplify


%28-2y%29%2F%28-2%29=%28-1x%2B7%29%2F%28-2%29 Divide both sides by -2 to isolate y


y+=+%28-1x%29%2F%28-2%29%2B%287%29%2F%28-2%29 Break up the fraction on the right hand side


y+=+%281%2F2%29x-7%2F2 Reduce and simplify


The original equation 1x-2y=7 (standard form) is equivalent to y+=+%281%2F2%29x-7%2F2 (slope-intercept form)


The equation y+=+%281%2F2%29x-7%2F2 is in the form y=mx%2Bb where m=1%2F2 is the slope and b=-7%2F2 is the y intercept.







Now let's find the equation of the line that is perpendicular to y=%281%2F2%29x-7%2F2 which goes through (0,-3)

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 1%2F2, 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%281%2F2%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%282%2F1%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-2%2F1 Multiply the fractions.


So the perpendicular slope is -2



So now we know the slope of the unknown line is -2 (its the negative reciprocal of 1%2F2 from the line y=%281%2F2%29%2Ax-7%2F2). 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=-2%2A%28x-0%29 Plug in m=-2, x%5B1%5D=0, and y%5B1%5D=-3



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



y%2B3=-2%2Ax-0 Multiply



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

y=-2%2Ax-3 Combine like terms

So the equation of the line that is perpendicular to y=%281%2F2%29%2Ax-7%2F2 and goes through (0,-3) is y=-2%2Ax-3


So here are the graphs of the equations y=%281%2F2%29%2Ax-7%2F2 and y=-2%2Ax-3




graph of the given equation y=%281%2F2%29%2Ax-7%2F2 (red) and graph of the line y=-2%2Ax-3(green) that is perpendicular to the given graph and goes through (0,-3)