Finding equation for line

[Destable]

Hello!

I hope this is in the right area. I have two points (4,6) and (-2,3), and I need to find the slope-intercept equation for these two points.

I started by finding the slope:

m = 3-6/-2-4 = -3/-6=-1/2 or -0.5

The equation I have to find the slope intercept form is

y - y1 = m(x - x1)

so I plug my numbers in:

y - 6 = -1/2(x - 4)

and I try to get it into slope intercept form of y = mx + b:

multiply by -2 to get rid of fraction, -2y - 12 = -1(x-4)
use distributive property -2y - 12 = -x + 4
add 12 to both sides -2y = -x + 16
divide by -2 again y = (-x/-2) -8

If you plug in the points, you will see this is obviously not right. I'm very confused as to what I am doing wrong, but I suspect it has something to do with the slope or I'm not handling the signs correctly. Please help!

[HallsofIvy]

Hello!

I hope this is in the right area. I have two points (4,6) and (-2,3), and I need to find the slope-intercept equation for these two points.

I started by finding the slope:

m = 3-6/-2-4 = -3/-6=-1/2 or -0.5

The equation I have to find the slope intercept form is

y - y1 = m(x - x1)

so I plug my numbers in:

y - 6 = -1/2(x - 4)

and I try to get it into slope intercept form of y = mx + b:

multiply by -2 to get rid of fraction, -2y - 12 = -1(x-4)
Here's your error. Are you multiplying by -2 or 2?
If you are multiplying by -2, it is -2(y- 6)= -2((-1/2)(x- 4) or -2y+ 12= x- 4.
If you are multiplying by 2, it is 2(y- 6)= 2(-1/2)(x- 4)= 2y- 12= -(x-4).

In either casy you get 2y= -x- 16

use distributive property -2y - 12 = -x + 4
add 12 to both sides -2y = -x + 16
divide by -2 again y = (-x/-2) -8

If you plug in the points, you will see this is obviously not right. I'm very confused as to what I am doing wrong, but I suspect it has something to do with the slope or I'm not handling the signs correctly. Please help!
It was a "signs" problem. You should have y= -(1/2)x- 8, not y= (1/2)x- 8

[Destable]

Thank you so very much!

While your answer did not contain the correct solution, it helped me to figure out what I was doing wrong and get the correct one!

In any case, the slope-intercept equation for those points would be y = 1/2x + 4

Again, thank you immensely!

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