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Write one equation of the line through the given points in slope-intercept form.Then rewrite the equation in standard form using integers.

The points are: (2,1) and (-2,-1)
                       (5,6) and (3,10)
                       (3,7) and (-2,5)

Comments

1)_ (2,1)&(-2,-1)

As m = Y2-Y1 / X2-X1, then

m = -1-1 / -2-2

m = -2 / -4

m = 1/2

Now we we either one points to find c from

Y = mX + c

putting the values of any points, we get

1 = (1/2)2 + c

1 = 1 + c

now we get c = 0

So now we put the values of c and m in the equation Y = mX + c to get equation in slope intercept form, then

Y = 1/2X + 0

Hence Y = 1/2X Or

2Y = X

2)_ (3,7)&(-2,5)

As m = Y2-Y1 / X2-X1, then

m = 5-7 / -2-3

m = -2/-5

m = 2/5

Now we we either one points to find c from

Y = mX + c

putting the values of any points, we get

7 = (2/5)3 + c
29/5 = c

now we get c = 29/5

So now we put the values of c and m in the equation Y = mX + c to get equation in slope intercept form, then

Hence Y = 2/5X + 29/5 Or
5Y = 2x =29

3)_ (5,6)&(3,10)As m = Y2-Y1 / X2-X1, then

m = 10-6 / 3-5

m = 4 / -2

m = -2

Now we we either one points to find c from

Y = mX + c

putting the values of any points, we get

6 = (-2)5 + c
6 = -10 + c

6 + 10 = c

c = 16

now we get c = 16

So now we put the values of c and m in the equation Y = mX + c to get equation in slope intercept form, then

Hence Y = -2X + 16 Or
Y = 16 - 2x

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