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.Com
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)   (Show Source): You can put this solution on YOUR website!
passes through the given point (8,-2)
and is perpendicular to the given line
the equation in slope-intercept form:



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 , you can find the perpendicular slope by this formula:

where is the perpendicular slope


So plug in the given slope to find the perpendicular slope



When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second



Multiply the fractions.


So the perpendicular slope is



So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). 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:

where m is the slope and (,) is the given point



Plug in , , and



Distribute



Multiply



Subtract from both sides to isolate y

Make into equivalent fractions with equal denominators



Combine the fractions



Reduce any fractions

So the equation of the line that is perpendicular to and goes through (,) is


So here are the graphs of the equations and




graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)
Answer by lwsshak3(11628)   (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
RELATED QUESTIONS

Write an equation for a line that is a) parallel and b) perpendicular to the given line... (answered by robertb)
write an equationfor the line that is perpendicular to the given line and that passes... (answered by subbbu,stanbon)
Write an equation of the line that passes through the given point and is perpendicular to (answered by stanbon)
write an equation of the line that is perpendicular to the given line and passes through... (answered by mananth)
write an equation of the line that is perpendicular to the given line and passes through... (answered by ReadingBoosters)
Write an equation of the line that is perpendicular to the given line and passes through... (answered by Cromlix)
Write an equation of the line that passes through the given point and is perpendicular to (answered by Alan3354)
Write an equation of the line that passes through point p and is perpendicular to the... (answered by stanbon)
Write an equation in slope-intercept form for the line that is perpendicular to the given (answered by robertb)
write an equation in slope intercept form for a line that passes through the given point... (answered by josmiceli)