SOLUTION: Please HELP me solve this quesion !!! A line passes through the points (2,9) and (9,2) ~ a. Write the equation of the line. b. Write the equation of the parallel line goin

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Please HELP me solve this quesion !!! A line passes through the points (2,9) and (9,2) ~ a. Write the equation of the line. b. Write the equation of the parallel line goin      Log On


   

Question 730051: Please HELP me solve this quesion !!!
A line passes through the points (2,9) and (9,2) ~
a. Write the equation of the line.
b. Write the equation of the parallel line going through the origin.
c. Write the equation of the perpendicular line through (2,9).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a.
the equation of the line passes through the points (2,9) and (9,2)

Solved by pluggable solver: FIND EQUATION of straight line given 2 points
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (2, 9) and (x2, y2) = (9, 2).
Slope a is a+=+%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29+=+%282-9%29%2F%289-2%29+=+-1.
Intercept is found from equation a%2Ax%5B1%5D%2Bb+=+y%5B1%5D, or -1%2A2+%2Bb+=+11. From that,
intercept b is b=y%5B1%5D-a%2Ax%5B1%5D, or b=9--1%2A2+=+11.

y=(-1)x + (11)

Your graph:





b.

the equation of the parallel to line y=-1x%2B11 going through the origin (0,0)

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 -1 (its from the slope of y=-1%2Ax%2B11 which is also -1). Also since the unknown line goes through (0,0), 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=-1%2A%28x-0%29 Plug in m=-1, x%5B1%5D=0, and y%5B1%5D=0



y-0=-1%2Ax%2B%281%29%280%29 Distribute -1



y-0=-1%2Ax-0 Multiply



y=-1%2Ax-0%2B0Add 0 to both sides to isolate y

y=-1%2Ax%2B0 Combine like terms

So the equation of the line that is parallel to y=-1%2Ax%2B11 and goes through (0,0) is y=-1%2Ax%2B0


So here are the graphs of the equations y=-1%2Ax%2B11 and y=-1%2Ax%2B0



graph of the given equation y=-1%2Ax%2B11 (red) and graph of the line y=-1%2Ax%2B0(green) that is parallel to the given graph and goes through (0,0)





c.
the equation of the perpendicular to line y=-1x%2B11 through (2,9)
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, 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%28-1%2F1%29 So plug in the given slope to find the perpendicular slope



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


So the perpendicular slope is 1



So now we know the slope of the unknown line is 1 (its the negative reciprocal of -1 from the line y=-1%2Ax%2B11). Also since the unknown line goes through (2,9), 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=1%2A%28x-2%29 Plug in m=1, x%5B1%5D=2, and y%5B1%5D=9



y-9=1%2Ax-%281%29%282%29 Distribute 1



y-9=1%2Ax-2 Multiply



y=1%2Ax-2%2B9Add 9 to both sides to isolate y

y=1%2Ax%2B7 Combine like terms

So the equation of the line that is perpendicular to y=-1%2Ax%2B11 and goes through (2,9) is y=1%2Ax%2B7


So here are the graphs of the equations y=-1%2Ax%2B11 and y=1%2Ax%2B7




graph of the given equation y=-1%2Ax%2B11 (red) and graph of the line y=1%2Ax%2B7(green) that is perpendicular to the given graph and goes through (2,9)





y=-1x%2B11...given line
y=-1x...parallel line
y=x%2B7...perpendicular

let's graph them all together:
+graph%28+600%2C+600%2C+-15%2C+15%2C+-15%2C+15%2C+-1x%2B11%2C-1x%2Cx%2B7%29+