SOLUTION: Find an equation of the line that passes through the given point and is perpendicular to the given line. Write the equation in slope-intercept form. (8, −2), 7x = 9y −

Algebra ->  Equations -> SOLUTION: Find an equation of the line that passes through the given point and is perpendicular to the given line. Write the equation in slope-intercept form. (8, −2), 7x = 9y −      Log On


   

Question 777596: Find an equation of the line that passes through the given point and is perpendicular to the given line. Write the equation in slope-intercept form.
(8, −2), 7x = 9y − 8
Found 2 solutions by MathLover1, lwsshak3:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
passes through the given point (8,-2)
and is perpendicular to the given line 7x+=+9y-+8
the equation in slope-intercept form:
7x%2B8+=+9y+
y=%287%2F9%29x%2B8%2F9++

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 7%2F9, 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%287%2F9%29 So plug in the given slope to find the perpendicular slope



m%5Bp%5D=%28-1%2F1%29%289%2F7%29 When you divide fractions, you multiply the first fraction (which is really 1%2F1) by the reciprocal of the second



m%5Bp%5D=-9%2F7 Multiply the fractions.


So the perpendicular slope is -9%2F7



So now we know the slope of the unknown line is -9%2F7 (its the negative reciprocal of 7%2F9 from the line y=%287%2F9%29%2Ax%2B8%2F9). Also since the unknown line goes through (8,-2), 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%2B2=%28-9%2F7%29%2A%28x-8%29 Plug in m=-9%2F7, x%5B1%5D=8, and y%5B1%5D=-2



y%2B2=%28-9%2F7%29%2Ax%2B%289%2F7%29%288%29 Distribute -9%2F7



y%2B2=%28-9%2F7%29%2Ax%2B72%2F7 Multiply



y=%28-9%2F7%29%2Ax%2B72%2F7-2Subtract -2 from both sides to isolate y

y=%28-9%2F7%29%2Ax%2B72%2F7-14%2F7 Make into equivalent fractions with equal denominators



y=%28-9%2F7%29%2Ax%2B58%2F7 Combine the fractions



y=%28-9%2F7%29%2Ax%2B58%2F7 Reduce any fractions

So the equation of the line that is perpendicular to y=%287%2F9%29%2Ax%2B8%2F9 and goes through (8,-2) is y=%28-9%2F7%29%2Ax%2B58%2F7


So here are the graphs of the equations y=%287%2F9%29%2Ax%2B8%2F9 and y=%28-9%2F7%29%2Ax%2B58%2F7




graph of the given equation y=%287%2F9%29%2Ax%2B8%2F9 (red) and graph of the line y=%28-9%2F7%29%2Ax%2B58%2F7(green) that is perpendicular to the given graph and goes through (8,-2)

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation of the line that passes through the given point and is perpendicular to the given line. Write the equation in slope-intercept form.
(8, −2), 7x = 9y − 8
***
Equation of a line: y=mx+b, m=slope, b=y-intercept
7x = 9y − 8
9y=7x+8
y=7x/9+8/9
slope of given line, m=7/9
slope of perpendicular line=-9/7 (negative reciprocal)
Equation:
y=-9x/7+b
solve for b using given coordinates(8,-2) on the line
-2=-9*8/7+b
-2=-72/7+b
b=58/7
Equation of perpendicular line:
y=-9x/7+58/7