how to write the equation given when in pairs. please help me understand?

Question

Write the equation of the line passing through each of the given points with the indicated slope. Give your results in slope-intercept form, where possible.
(-1,3) and (4, -2) (2, -3) and (2, 4)

Answer 1

m = (- 2 - 3) / (4 + 1) = - 5 / 5 = - 1
Line with this gradient(slope) passes thro` (-1,3) and all other given points.
y - 3 = (-1) (x + 1)
y - 3 = - x - 1
y = - x + 2

Answer 2

To create a linear equation in slope-intercept form you need to know of the generic version of it:

y = mx + b, where x and y are your variables, m is the slope, and b is the intercept.

Now first we need to find the slope which is just the change in y over the change in x:

(3 - -2) / (-1 - 4) = 5/-5 = -1

Now we substitute that for m:
y = -x + b

Now we take a point and substitute the values for the variables and solve for b:

(-1, 3) >>> (3) = -(-1) + b
3 = 1 + b
2 = b

Now we write the completed equation:
y = -x + 2

I'm sure you can do the next one.

Answer 3

(i) First find the equation of any line passing through the two given points. The equation of the line is given below:-

(y-y')=[(y"-y')/(x"-x')][x-x']

This is the General equation passing through two points (x',y') and (x",y")

The verify whether the line passes through the other two points.

(ii) To transform any equation of line in the slope-intercept form, isolate y on one side and take x on other side to be reduced to the form

y = mx + c