write an equation in slope-intercept form #3?

Question

Write an equation in slope-intercept form
through (4, -4) and (-2, 2)
Correct answer y= -x (please help me to understand how to get to this answer, studying for mid-term)

Answer 1

Because we don't know what the y-intercept is yet, the best way will be to use the point-slope form, and put that into slope-intercept form.

Point-slope form is y - Y = m(x - X) where (X, Y) is a point on the line. We know two points, so the only thing we need is m, the slope.
Slope is (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the line.
Let (x1, y1) = (4, -4) and let (x2, y2) = (-2, 2).
m = (2 - -4) / (-2 - 4) = (2 + 4) / (-2 - 4) = 6 / (-6) = -1
Let's use (-2, 2) for (X, Y). Our line then is
y - 2 = -1(x - -2)
y - 2 = -(x + 2)
y = (-x - 2) + 2
y = -x

Answer 2

well, first we need to find the slope of the line by using the formula:
(y2-y1) ||||||| (2-(-4)) |||| 6
---------- = ----------- = ----- = -1
(x2-x1) ||||||| (-2-4) ||||| -6

now that we know that the slope of the line is -1, we can use one of the points that we know the graph passes through and substitute these numbers into the standard slope-intercept form equation y=mx+b:
2=(-1)(-2)+b
2=2+b
0=b

therefore the equation of the line is y=-x+0 which simplifies to:
y=-x

Answer 3

Slope is (2-(-4))/(-2-4) = -1

Intercept is 0, passes through origin

Thus form is y=-x.

Answer 4

First you need to find the slope which is m= y2-y1/x2-x1.

Let (y1,x1)=(4,-4) and (y2,x2)=(-2,2). Once you find m, you can solve y-y1=m*(x-x1) and rewrite so that y is the subject of the formula.

Answer 5

let (4,-4) be (x1,y1) and (-2,2) be (x2,y2)
m= (y2-y1)/(x2-x1)
So
(y-y1)=m(x-x1) (point slope form)
thus
(y-(-4))=(2-(-4))/(-2-4) * (x-4)
y+4 = 6/(-6) *(x-4)
y+4 = -(x-4)
y+4 = -x+4
y = -x

Answer 6

working...