Find the equetion of the line that passes though A( -1, 3 ) and B( 2, -1 )?

Answer 1

m = (-1 - 3) / (2 + 1)
m = - 4 / 3
y - 3 = (- 4 / 3) (x + 1)
y = (- 4 / 3) x - 4 / 3 + 3
y = (- 4 / 3) x + 5 / 3
3 y = - 4x + 5
4x + 3y - 5 = 0

Answer 2

Straight line equation:

y = mx + b, where:

m=slope,
b=y-intercept

Slope, m, is given by:

m = (y2 - y1)/(x2 - x1), where

y2 = -1
y1 = 3
x2 = 2
x1 = -1

Plug these in slope equation to get m:

m = (-1 - 3)/(2 - (-1)) --> m = -4/3

Your straight line equation now looks like this:

y = (-4/3)x + b

To find b, plug x=-1 and y=3 in the above equation and... solve for b:

3 = (-4/3)(-1) + b ---> 3 = 4/3 + b -->
b = 3 - 4/3 ---> b = 9/3 - 4/3 ---> b = 5/3

So, your straight line equation is:

y = (-4/3)x + 5/3

Verify by plugging in x=2. You should get y=-1:

y = (-4/3) 2 + 5/3 = -8/3 + 5/3 = -3/3 = -1

Checks out :-)

Answer 3

y= (rise/run)*x + y intercept rise=Δy run=Δx

Δy= y2-y1 = -1-3=-4
Δx= x2-x1 =2-(-1)=2+1=3
slope=(rise/run)=-4/3

y intercept = y when x=0
as 1=1/3*3 because the difference between -1 and 0 =1

(-4/3)/(3/3)= stays the same as last time =-1 and a third

so y= -4/3x + (3-(1+1/3))=-4/3x+(9/3-4/3)

solve the last part to find the equation not the equetion

Answer 4

You must reach an expression like
y=mx+b

So, to determine m first you must do
AB= B-A = (2+1, -1-3) =(3,-4)
So your m is =-4/3

So, now you have y=-4/3 x +b
To find b you must pick one of the points and susbtitute it in your equation

I picked A
3= -4/3 *-1+b
3= 4/3 +b
3-4/3 =b
9/3-4/3 =b
b=5/3

So, your line can be
y=-4/3 x +5/3

Answer 5

You must reach an expression like
y=mx+b

So, to determine m first you must do
AB= B-A = (2+1, -1-3) =(3,-4)
So your m is =-4/3

So, now you have y=-4/3 x +b
To find b you must pick one of the points and susbtitute it in your equation

I picked A
3= -4/3 *-1+b
3= 4/3 +b
3-4/3 =b
9/3-4/3 =b
b=5/3

So, your line can be
y=-4/3 x +5/3

Answer 6

Find the slope(A), put it into the equation Y = Ax + B, then plug in one of the points to find B

A = (-1 - 3) / (2 - (-1)) = -4 / 3
y = (-4/3)*x + B
Plug in one of the points
3 = (-4/3)*(-1) + B
3 = 4/3 + B ========> B = 5/3

y = (-4/3)x + 5/3

Answer 7

the gradient is (y1-y2) divided by (x1-x2)=(-1-3) divided by (2+1)= -4/3

then use the formula, y-y1=m(x-x1)
then y-3=-4/3(x+1)
y= -4/3x-4/3+3
y= -4/3x +5/3
to make it simpler, it becomes 3y=-4x +5

Answer 8

y=-4/3x + 5/3