Question

Write the equation on a line that is perpendicular to the given line and passes through the given point.
y - 4 = 5/2(x+3);(-3,4)
A. y+4=-2/5(x-3)
B. y-3=-2/5(x+4)
C. y-4=-2/5(x+3)
D. y+4=2/5(x-3)

Answer 1

@sweetburger

Answer 2

actually, since it's already in slope intercept form all you need to do is find what the slope is. since you're given 5/2 as the slope just find the negative reciprocal of that.

Answer 3

sorry point slope form* m(x-x0) = y-y0

Answer 4

I dont understand

Answer 5

Do you still need help with this problem?

Answer 6

yes

Answer 7

@mathstudent55 ???

Answer 8

There are several ways of determining a single line.
For example, if you are given two different points, there is only one line that passes through them, so you can find the equation of a line.
Another example is if you are given a point and a slope. If you have a point and a slope, there is only one line that passes through a given point with a given slope, so you can also find its equation.

Answer 9

Your case is like the second example.

Answer 10

And, what everyone is forgetting to tell you, is that if you know the slope of a line, you can find the slope oft he perpendicular lines.
Take the slope of the given line, m1. Write as a fraction, a/b.
(If m1= 1/3, then a=1 and b=3. If m1 = -4, then a = -4 and b=1)
A perpenicular line has slope m2 = -b/a

Answer 11

You are given a point that the line goes through, (-3, 4).
You are not given a second point, but you are told the line is perpendicular to a given line.
You can take the given line and use it to find the slope of a perpendicular to it.
Then you use the slope of the perpendicular that you find and the given point to find the equation of the line.

Answer 12

Here is the equation you are given.

Let's put it in the slope-intercept form so you can see easily its slope.
We solve for y, and put it in the y = mx + b form, where m is the slope.

\(y - 4 = \dfrac{5}{2}(x+3)\)

\(y - 4 = \dfrac{5}{2}x+\dfrac{5}{2} \times 3\)

\(y = \dfrac{5}{2}x+\dfrac{15}{2} + 4\)

\(y = \dfrac{5}{2}x+\dfrac{15}{2} + \dfrac{8}{2}\)

\(y = \dfrac{5}{2}x+\dfrac{23}{2} \)

We see that the slope of the given line is 5/2.

Now we need the negative reciprocal of that slope since the slopes of perpendicular lines are negative reciprocals. To find the negative reciprocal, just flip the fraction and change the sign.

The negative reciprocal of 5/2 is -2/5

Answer 13

Now you know a point and the slope of the new line. You can find its equation.

Answer 14

You can use the point-slope form:

\(y - y_1 = m(x - x_1)\)

Substitute m with your slope, -2/5, and substitute \(x_1\) and \(x_2\) with the x- and y-coordinates of your point (-3, 4), respectively.

Answer 15

I'm really confused if its that equation then what would the answer be because I see no answer lilke that

Answer 16

Did you "Substitute m with your slope, -2/5, and substitute x1 and x2 with the x- and y-coordinates of your point (-3, 4), respectively." If you show us that work, we can help you get it into a form like your answer.

Answer 17

ughhhh its tooken so long to just answer a question

Answer 18

Had to go live my real life. And I don't do short answers. :-)
Here now though; can you tell where you are stuck?

Answer 19

"y - 4 = 5/2(x+3)" is the given equation of a straight line.
You can read the slope of this straight line directly from this equation. What is it? Call it m.

Then the slope of a line perpendicular to the given line is the negative reciprocal of m:\[m _{perpendicular~line}=-1/m\]

So, you now have the slope of the perpend. line and you have one point on that line. What ist he equation of the line? Use the slope you've just found and the point specified in the original problem statement.

Answer 20

Thanks :)