SOLUTION: (1,5) and (3,13) a) list 2 equations for parellel lines b) find the eqaution of the perpendicular line c) graph the perpindicular line

Algebra ->  Graphs -> SOLUTION: (1,5) and (3,13) a) list 2 equations for parellel lines b) find the eqaution of the perpendicular line c) graph the perpindicular line       Log On


   

Question 387806: (1,5) and (3,13)

a) list 2 equations for parellel lines
b) find the eqaution of the perpendicular line
c) graph the perpindicular line
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+2x%2B5 and -2x%2By+=+-2+ are parallel+ lines
since the slope of the line y+=+2x%2B5 is 2,
and the slope of the line -2%2Ax%2By+=+-2 is 2,
these lines are parallel since a parallel line has an identical slope.
intercept points:
x intercept is found by setting y+to 0:
ax%2Bby=c becomes ax=c..... that means that x+=+c%2Fa
in your case -2x+=5 and intercept x+=+-5%2F2=-2.5
point is (-2.5,0)
y intercept is found by setting x to 0: the equation becomes by=c, and therefore y+=+c%2Fb, so y intercept is 5%2F1+=+5
point is (0,5)
Slope is m=-2%2F1+=+-2.

For the perpendicular line, you have to find the perpendicular slope. The reference slope is m+=+2, and, for the perpendicular slope, you will flip this slope and change the sign. Then the perpendicular slope is
m1=-1%2F2+

So now you can do the point-slope form.
point is (0,5), and m1=-1%2F2+
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, 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%2F1%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%281%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=-1%2F2 Multiply the fractions.


So the perpendicular slope is -1%2F2



So now we know the slope of the unknown line is -1%2F2 (its the negative reciprocal of 2 from the line y=2%2Ax%2B5). Also since the unknown line goes through (0,5), 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-5=%28-1%2F2%29%2A%28x-0%29 Plug in m=-1%2F2, x%5B1%5D=0, and y%5B1%5D=5



y-5=%28-1%2F2%29%2Ax%2B%281%2F2%29%280%29 Distribute -1%2F2



y-5=%28-1%2F2%29%2Ax-0%2F2 Multiply



y=%28-1%2F2%29%2Ax-0%2F2%2B5Add 5 to both sides to isolate y

y=%28-1%2F2%29%2Ax-0%2F2%2B10%2F2 Make into equivalent fractions with equal denominators



y=%28-1%2F2%29%2Ax%2B10%2F2 Combine the fractions



y=%28-1%2F2%29%2Ax%2B5 Reduce any fractions

So the equation of the line that is perpendicular to y=2%2Ax%2B5 and goes through (0,5) is y=%28-1%2F2%29%2Ax%2B5


So here are the graphs of the equations y=2%2Ax%2B5 and y=%28-1%2F2%29%2Ax%2B5




graph of the given equation y=2%2Ax%2B5 (red) and graph of the line y=%28-1%2F2%29%2Ax%2B5(green) that is perpendicular to the given graph and goes through (0,5)



so, the line y=%28-1%2F2%29x+%2B5 is perpendicular to given line y+=+2x%2B5 and to its parallel line -2x%2By+=+-2+