What is equation of the blue line

 y = -1x - 1

Step-by-step explanation:

Before we start remember that the formula/equation of a line is:

                                       y = mx + b

What are these random letters doing in math? As if math wasn't hard enough with numbers! Now we add numbers in? Oh, this world is a cruel place!

Now, now let's all remain calm! There is a good reason for this! But first we must understand what those letters represent in the first place!

Now, if you have seen more than just this formula to find slopes, (meaning different forms of an equation) than you are right! There are different ways but I'm not going to get into that too much.

But onto our quest to find the y-intercept and the x-intercept for fun! If we look closely we can find that the x-intercept is -1 and the y-intercept is also -1! Now our equation is still missing our slope! But before we find it let's add new information to our equation:

                                                  y = mx + -1

Ok let's find m!

The formula for finding m is:

                                                     y = mx + (-1)

I know what your thinking it's the same exact thing!

And yes you are correct!

In order to find the slope though we must take one point any point on the blue line. On this line there are two points which are, (-1 , 0) and (0 , -1).

REMEMBER

When plotting points you will ALWAYS write them in this form (x-intercept, y-intercept)

Carrying on, I will use the point (-1 , 0). Let's substitute!

                                      y = m × x + (-1)

We get,                        

                                     0 = m × (-1) - 1

Add 1  on both sides,

                                      1 = -m

If 1 is what -m is equal too we still haven't found out what m is! I know to some people this will be a simple step but this is the logic behind it:

Multiply -1 on both sides,

                                     (-1) × 1 = (-1) × (-m)

Our result after a lot of effort is:

                                          -1 = m

Don't celebrate yet! We still need to put together the equation! Let's do a before and after eh?

BEFORE:

                                             y = mx + b

AFTER:

                                             y = -1x - 1

Alright we are done

Nice job everyone! LET'S CELEBRATE

Everyone form a line!

Now scream, "WE FINISHED THE PROBLEM"