Help: Find line perpendicular to y=-2/3x-8/9 passing thru (6,-9)

[confused1212]

hi guys can someone answer this: write the equation perpendicular to y=-2/3x-8/9 and which passes through (6,-9)

 

[lev888]

hi guys can someone answer this: write the equation perpendicular to y=-2/3x-8/9 and which passes through (6,-9)

Google should find a lot of matches for "equation of line through point and perpendicular to line".

 

[Dr.Peterson]

hi guys can someone answer this: write the equation perpendicular to y=-2/3x-8/9 and which passes through (6,-9)

There are a couple ways to approach the details. What have you learned about this topic? We'll also want to see what work you have done, so we can see where you need help.

If you haven't yet read our guidelines for submission, please do so. They are important.

 

[Steven G]

hi guys can someone answer this: write the equation perpendicular to y=-2/3x-8/9 and which passes through (6,-9)

Hi, welcome to the forum. I am sorry but we do not offer that type of service here. We do offer help and that is why we need to see your work so we know where you are stuck.

I will give you a start by saying that the slope of perpendicular lines have a product of -1. What is the slope of the line y=-2x/3-8/9? Then multiply this slope by m and set it equal to -1 and solve for m. For example, IF the slope of y=-2x/3-8/9 is 7/5, solve (7/5)m =-1 for m

Please find the slope and if you need help with that or with the next step then reply back.

 

[sinx]

hi guys can someone answer this: write the equation perpendicular to y=-2/3x-8/9 and which passes through (6,-9)

to find a perpendicular slope.
https://www.mathwarehouse.com/algebra/linear_equation/parallel-perpendicular-lines.php

 

[pka]

hi guys can someone answer this: write the equation perpendicular to y=-2/3x-8/9 and which passes through (6,-9)

I am a strong proponent of using the general form of the line: \(\displaystyle Ax+By+C=0\)
Using that equation we can see at once the slope: \(\displaystyle \dfrac{-A}{B},~B\ne 0\).
Moreover, any other line \(\displaystyle Ax+By+T=0\) is parallel because it has the same slope.
AND the line \(\displaystyle Bx-Ay+P=0\) is perpendicular to the original.

In this case, the general form of your line is \(\displaystyle 6x+9y+8=0\)
So the line \(\displaystyle 9x-6y+P=0\) is perpendicular to your line, for any \(\displaystyle p\).
But how do we make it pass thru \(\displaystyle (6,-9)~?\) Well \(\displaystyle P=-[9(6)-6(-9)]\).
DONE

 

[sinx]

hi guys can someone answer this: write the equation perpendicular to y=-2/3x-8/9 and which passes through (6,-9)

pka gives a nifty way to solve the problem, using the general eqn of a line, but it is easier for me to understand using the defn of slope.

in any case, you must first recognize that perpendicular slopes are negative reciprocals.
e.g. the line y=-2/3x-8/9 has a slope of -2/3
the negative reciprocal of -2/3 = 3/2

so you need an eqn of a line with slope 3/2 that passes thru (6,-9)
defn of slope=(y₂-y₁)/(x₂-x₁)
plug in the numbers;
3/2=(y₂-(-9))/(x₂-6)

3/2=(y-(-9))/(x-6) [ignore the subscripts]
reduces to;
y=3/2x-18

i encourage you to prove to yourself that perpendicular lines have negative reciprocal slopes.
graph these two perpendicular lines, plus slopes of 2 and -1/2, then 3 and -1/3, and so on.
then you will understand, versus just trying to remember.

 

[jtayag0622]

By definition, the slopes of two perpendicular lines are opposite reciprocal of each other, which means you have to take the opposite sign of the first slope then reciprocate it. You can use that fact to solve for the other equation using the point-slope formula or the slope-intercept form.

The slope of y=-2/3 x-8/9 is -2/3
The slope of the second equation should be 3/2

point-slope formula: y-y_1=m(x-x_1)

The second equation should pass through (6,-9), so substitute the values and solve.

y+9=3/2(x-6)

y=3/2 x-18

Slope-intercept form: y=mx+b

Since we already know the slope, we just have to plug in the values of x and y to solve for b

-9=3/2(6)+b
b=-18

Then plug it in back to the equation:

y=3/2 x-18

That’s how to solve for the equation of the line perpendicular to another line. These are also the methods we use for parallel lines. Choose the method that best fits you.