I am stumped! I have been working on these problems for the longest time and I can not figure out what I am doing wrong. Some how when I get to the last two steps I mess up, and I am beyond frustrated.
The directions say:
Write an equation of the line containing the given point and perpendicular to the given line.
1. (-5,9) 5x=6y+7
2. (3,5) 4x+y=9
3. (3,-5) 6x+5y=7
To show you where I am messing up I am going to give you one I have already tried to do, then maybe someone can tell me where I am going wrong. I have a test on this tomorrow and I don't get it at ALL!
(4,6) x+9y=7
y= -1/9-7/9
Then you use the formula y-y1=m(x-x1)
so it would be
y-6=-1/9x+4
Then here is where I am having problems, when I try to multiply the -1/9 by 4 and then add 6 to it, I come up with the wrong answer.
I got y= -1/9x+10/9. The right answer is -1/9x+58/9. The answers all have to be in the formula of y=mx+b
Thanks for your help!
Start here: you have the general equation correct..
y= -x/9 -7/9
Now you want a line perpendicular to this line, so it has the slope 9 (negative reciprocal of -1/9
So the equation of the perpendicular is
y=9x + b.
Put in the point 4,6
6=9*4+b so b= -30
so the answer is y=9x-30. That is the equation of a line perpendicular and through the point 4,6. Your stated right answer is wrong.
One more:
(-5,9) 5x=6y+7
y=5/6 x -7/6
so the perpendicular line will be slope -6/5, or
y=-6x/5 +b
put in the point (-5,9)
9=30/5 + b
or b=3
y=-6x/5 + 3 is the equation of the line perpendicular containing the point.
It seems like there might be some confusion in the steps you are taking to solve these problems. Let's go through the process step by step to make sure we get the correct answer.
To find the equation of a line perpendicular to a given line, we need to first find the slope (m) of the original line. The slope of a line can be determined from its equation in the form y = mx + b, where m is the slope.
1. (-5,9) 5x = 6y + 7:
To find the slope of this line, we can rearrange the equation to the form y = mx + b:
6y = 5x - 7
y = (5/6)x - 7/6
The slope of this line is (5/6).
Since the line we want to find is perpendicular to this line, its slope will be the negative reciprocal of (5/6). The negative reciprocal is found by flipping the fraction and changing its sign, so the slope of the line we want to find is (-6/5).
Now that we have the slope of the new line, we can use the point-slope form of the equation to find the equation of this line:
y - y1 = m(x - x1)
Substitute the values of the point (-5,9) and the slope (-6/5) into the equation:
y - 9 = (-6/5)(x - (-5))
Simplify and solve for y:
y - 9 = (-6/5)(x + 5)
y - 9 = (-6/5)x - 6
y = (-6/5)x + 3
So, the equation of the line containing the point (-5,9) and is perpendicular to 5x = 6y + 7 is y = (-6/5)x + 3.
Similarly, you can follow these steps to solve the remaining two problems:
2. (3,5) 4x + y = 9:
Rearrange the equation to the form y = mx + b:
y = -4x + 9
The slope of this line is (-4), and the slope of the line we want to find is the negative reciprocal, which is (1/4).
Using the point-slope form with the point (3,5) and the slope (1/4), we get the equation of the line as y = (1/4)x + (17/4).
3. (3,-5) 6x + 5y = 7:
Rearrange the equation to the form y = mx + b:
5y = -6x + 7
y = (-6/5)x + 7/5
The slope of this line is (-6/5), and the slope of the line we want to find is the negative reciprocal, which is (5/6).
Using the point-slope form with the point (3,-5) and the slope (5/6), we get the equation of the line as y = (5/6)x - (35/6).
Remember to double-check your work during each step to ensure your calculations are correct. Good luck with your test!