find the equation of the lline through the points?

Question

(4, -4) (-2, -1)

Answer 1

Slope Formla

m = y₂- y₁/ x₂- x₁

Ordered Pairs

(4, - 4)(- 2, - 1)

m = - 1 - (- 4) / - 2 - 4

m = - 1+ 4 / - 6

m = 3 / - 6

m = - 1/2

-- - - - - - - --

Slope intercept form

y = mx + b

- 4 = - 1/2(4) + b

- 4 = - 4/4 + b

- 4 = - 1 + b

Transpose 1

- 4 + 1 = - 1 + b + 1

- 3 = b

- - - - - - - -

The equation

y = 1/2x - 3

- - - - - - - -s-

Answer 2

Let the equation be:
y = mx + c
Then:
y = (-1 - (-4) )x / (-2 - 4) + c
y = 3x/(-6) + c
y = -x/2 + c .........(1)
When x = 4, y = -4:
-4 = -4/2 + c
c = -2
Substitute this in (1):
y = -x/2 - 2.

Answer 3

y-y1
----- = gradient
x-x1

m = [-1-(-4)]/[-2-4] = 3/-6 = -1/2

y-(-4) = m(x-4)
y+4 = m(x-4)
y+4 = -1/2(x-4)
y = -1/2x + 2 -4 = -1/2x - 2

Did this fairly quickly.

Answer 4

gradient m = [ (- 1) - (- 4) ] / [(- 2) - 4 ]
m = 3 / (- 6)
m = (- 1 / 2)
y - (- 4) = (- 1 / 2).(x - 4)
y + 4 = (- 1 / 2).x + 2
y = (- 1 / 2).x - 2

Answer 5

m=DY/DX=3/-6=-1/2
EQ. is y+4=-1/2(x-4)
2y+8=-x+4
x+2y+4=0
verified.OK

Answer 6

Find the slope

y2 - y1 / x2 - x1 = m

y - y1 = m(x - x1) is the equation of the line

x1 y1
4 - 4

x2 y2
-2 -1

plug in the numbers, it's dead easy

Answer 7

y-y0=a(x-x0)

a=(dy/dx)
a=(-1-(-4))/(-2-4)=3/-6=-0.5

y-(-4)=-0.5(x-4)
y=-0.5x-2