HEEELLLPPPP
Identify the correct slope and y-intercept of the equation 2x + 3y = 6

Question

theeric · Answer

Hi! Are you ready? I'll guide you through it if you'd like.

anonymous · Answer

ya and after can you help me with other questions?

theeric · Answer

Possibly! We'll see about that after this. I'll likely be able to help :)

anonymous · Answer

ok

theeric · Answer

$$y=mx+b$$
Does this formula look familiar?

anonymous · Answer

ya

anonymous · Answer

if u can i really need help quickly

theeric · Answer

Cool! in$$y=mx+b$$ we have some variables.
m = the slope (so you will want to find this)
b = the y-intercept (so you'll want to find this)
x, y = the x and y coordinates of any point on the line (you'll leave these as x and y)

Not too hard! You already have an equation for the line. Since it's a line, we can it's equation look like$$y=mx+b$$, or$$y=?x+?$$, if you prefer.

theeric · Answer

So we'll use algebra on the equation you have, to make it look like y=mx+b.

theeric · Answer

I see that "y" in "y = mx + b" is on the left side. Lets start by doing that!

theeric · Answer

$$2x+3y=6$$

theeric · Answer

Would you like to suggest the first move?

theeric · Answer

I hope you understand the concept of "adding to both sides", "subtracting from both sides", "multiplying both sides", and "dividing by both sides".
When you alter each side in the same way as the other, then both new sides are still equal.
The new sides changed from what they were before, so they are not equal to what they were before, but what really matters is that you know the new sides are truely equal and you can use the new equation to go on.

Case and point,
$$2x+3y=6$$
Subtract "2x" from both sides
$$\rightarrow$$
$$2x-2x+3y = 6-2x$$
$$=3y=6-2x$$
Divid "3" from both sides
$$\rightarrow$$
$$\frac{3y}{3}=\frac{6-2x}{3}$$
$$=y=\frac{6}{3}-\frac{2}{3}x$$
$$=y=2-\frac{2}{3}x$$

Does it look familiar yet? Now we just switch the "2" with the "(2/3)x", and

$$y=-\frac{2}{3}x+2$$
compared to
$$y=mx+b$$
So you see where your "m" (slope) and "b" (y-intercept) is?
You can tell what the slope is because it is what is multiplied by x, and the y-intercept is the remaining term, when you set the equation equal to y.