# Help with the slope intercept form

#### skooter

##### New member
I'm stuck again! drat this book with little explanation and simple examples

I want to make sure im using the form correctly.

What is the slope of the line given by 2x+20=4y

would it then be 4y=2x+20

b=20 (or would I multiply that by 4 since it's 4y?)

m=-2

so the y-intercept would be either be 0,20 or 0,80 if I'm doing this correctly and the slope would be -2/1? I'm confusing myself the more I type so I'm gonna stop now

This is a tough subject for me and as I've stated earlier I don't have much help from a teacher since I'm taking this subject in Independent Study and this book sucks for explanations. Any help would be appreciated =)

Thanks

#### galactus

##### Super Moderator
Staff member
slope intercept form is y=mx+b

m is slope and b is the y-intercept.

You have $$\displaystyle 4y=2x+20$$

Divide through by 4 to solve for y:

$$\displaystyle y=\frac{2x+20}{4}=\frac{1}{2}x+5$$

Therefore, the slope is m=1/2 and the y-intercept is 5.

#### skooter

##### New member
Thanks,

That's much more clear than the book explanation.

So for 5y - 15 = 3 I would get:

-15x + 3 / 5 = -3/1 slope and 3/5 y intercept. Is this correct?

If it's not be patient with me, I'm a little algebra challenged lol.

#### skooter

##### New member
Also if I were to get a slope of lets say 5/5 would the slope be 5 rise and 5 run or 1 rise and 1 run since 5/5 = 1/1?

P.S.

#### galactus

##### Super Moderator
Staff member
It would be 5 over and 5 down, but the slope would be 1.

#### galactus

##### Super Moderator
Staff member
By using LaTex. Click on quote in the upper right hand corner of my post to see the code I used.

#### galactus

##### Super Moderator
Staff member
skooter said:
Thanks,

That's much more clear than the book explanation.

So for 5y - 15x = 3 I would get:

-15x + 3 / 5 = -3/1 slope and 3/5 y intercept. Is this correct?

If it's not be patient with me, I'm a little algebra challenged lol.
You're good, except for the minus sign.

$$\displaystyle 5y-15x=3$$

$$\displaystyle 5y=3+15x$$

$$\displaystyle y=\frac{3}{5}+3x$$

Your equation is $$\displaystyle 3x+\frac{3}{5}$$

It has slope 3 and y-intercept 3/5

#### skooter

##### New member
That's where I thought I might screw up.

So where does the minus come into the equation? Am I reversing it to be positive since the equation is solved in reverse? If that's the case wouldnt the first problem be

$$\displaystyle y= \frac {2x-20} {4}$$

$$\displaystyle y= \frac {2x+20} {4}$$

#### jonboy

##### Full Member
skooter said:
That's where I thought I might screw up.

So where does the minus come into the equation? Am I reversing it to be positive since the equation is solved in reverse? If that's the case wouldnt the first problem be

$$\displaystyle y= \frac {2x-20} {4}$$

$$\displaystyle y= \frac {2x+20} {4}$$
Since you are trying to islolate the y we added that 15x to both sides (Addition Property). We didn't reverse anything.

#### galactus

##### Super Moderator
Staff member
What minus?. I don't see a minus in the final equation.

I believe you're making this stuff harder than it needs to be.

Let me give you a small tutorial. As was stated, y=mx+b is slope-intercept form. m=slope and b=where it crooses the y-axis.

Let's say you have the points (2,3) and (-5,4) and you want to know the equation for the line passing through those points.

Slope is rise/run. You knew that, though.

$$\displaystyle \frac{4-3}{-5-2}=\frac{-1}{7}$$

m=slope=-1/7

Using our coordinates (-5,4) in the y=mx+b

$$\displaystyle 4=\frac{-1}{7}(-5)+b$$

Solve for $$\displaystyle b=\frac{23}{7}$$

You could also use (2,3) and get the same thing.

So, our equation is $$\displaystyle y=\frac{-1}{7}x+\frac{23}{7}$$

Now, in standard form it would be:

$$\displaystyle y+\frac{1}{7}x-\frac{23}{7}$$

Same thing, only in a different format.

#### skooter

##### New member
O.K thanks Jonboy and Galactus I understand now

And thanks for the TeX example Galactus now when I cry and scream for help I can do it in a neat way :lol:

#### jonboy

##### Full Member
skooter said:
O.K thanks Jonboy and Galactus I understand now

And thanks for the TeX example Galactus now when I cry and scream for help I can do it in a neat way :lol:
Lol your welcome and have a good day knowing you learned something.

#### galactus

##### Super Moderator
Staff member
Very good. We're glad you learned something. Once this line equation thing clicks, you'll see how simplistic it really is.