Question

Write the standard form of the line that passes through the given points.

Answer 1

First of all, remember what the equation of a line is:

y = mx+b

First, let's find what m:
m =   1-(-3) / 2-(-1)
m = 4/3

so: y = 4/3x + b

Now, what about b, or the y-intercept?

To find b, think about what your (x,y) points mean:
(-1,-3).
When x of the line is -1, y of the line must be -3.
(2,1).
When x of the line is 2, y of the line must be 1.

Now, look at our line's equation so far: y=4/3x+b. 

You can plug either (x,y) point you want into the x and y variables..the answer will be the same:
(-1,-3)
 -3=4/3 × -1+b,
b=-3-(4/3)(-1)
b=-5/3

(2,1)
1=4/3 × 2+b
b=1-(4/3)(2).
b=-5/3.
In both cases we got the same value for b.

So we have y = 4/3x -(5/3).

In standard form it would be:
(4/3)x - y = (5/3)