# 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.

How do you make your equations look so neat in your reply? #### galactus

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

#### galactus

##### Super Moderator
Staff member
How do you make your equations look so neat in your reply? 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.