Question

PLEASE HELP! I'LL FAN OR WHATEVER!
Indicate in standard form the equation of the line passing through the given points.

R(3, 3), S(-6, -6)

Answer 1

Let's sketch out these points.

Answer 2

Do you know y-form? I usually prefer to start in y-form, then solve into standard form. If you don't know it, then I won't try to confuse you.
Ergo, do you know this equation?
y = mx + b

Answer 3

Yes i know that equation.

Answer 4

Alrighty. So, we have two points, which makes it pretty easy to find the slope of the line using our fancy equation:
$$m = \frac{y_2 - y_1}{x_2-x_1}$$

Answer 5

Letting:
$$(x_1, y_1) = (3, 3) \\
(x_2, y_2) = (-6, -6)$$

Answer 6

We plug this into the slope formula to get
$$\frac{-6 - 3}{-6 - 3} = \frac{-9}{-9} = 1$$
So, the slope is 1.

Answer 7

Now, to find b in the equation y = mx + b, we just plug everything else back into the equation and solve for b. We can select any point we want to treat as (x, y). It works out, because this point is on the line, thus satisfying the requirements of the equation.
Enough talking, here's what I mean:
y = mx + b
We just found out the slope (m) is 1.
y = x + b
We know a point (x, y) that satisfies this line: (3, 3).
3 = 3 + b
0 = b
So, there is no b. This means the line equation is y = x

Answer 8

However, this is still in y-form. Standard form is:
Ax + By = C
The equation y = x is actually pretty easy to get in this form.
y = x
y - x = 0
or
-x + y = 0
This is in the form Ax + By = C, because A = -1, B = 1, and C = 0.
Congladurations.

Answer 9

Ah! So much work for a lazy person!! I have 30+ of these problems to do :/ But thank you so much for explaining everything!!
Sir, you are my hero.
Carry on.

Answer 10

This is actually the easiest way IMO. Some weird people will try to tell you to use a nonsense "point-slope" equation, which just makes things more complicated.
This way is completely intuitive; I pretty much just figured it out on my own, and if you're struggling in a test you could probably understand what to do just by thinking about the line and the slope equation and stuff.
However, if you want to be Ms. Algorithm and Fact, you just use this process:
#1.) Find the slope between the points.
#2.) Plug the slope into 'm' of the equation y = mx + b.
#3.) Take that new equation, and substitute any points (x, y).
#4.) Solve for b.
#5.) You now have your equation. Solve into any other form if necessary by just moving the terms around with the properties of algebra.