Can somebody please explain "Slope Intercept Form" to me?!?

Question

I have a horrible math block, so can you try to explain it almost child-like to me?!?! Step-by-step with nothing left out if possible. I have tried to learn it on my own and am still having trouble with it. I have a test on Tuesday!!! Thank you so much in advance for any help!!!

Here's an example...

3x + 5y = -15 <---That's a negative 15!

Thank you!!!

Answer 1

Without a question to go on, let's start at something very basic.

It takes two points to define a line. Any two points can have one and only one line drawn that intersects both points.

Now, the slope of the line is equal to the difference of the y coordinates divided by the difference of the x coordinates.
So for (X1,Y1) and (X2,Y2) the slope is ((Y2-Y1)/(X2-X1)).
In practical terms, if the points are (-3,-3) and (3,3) the slopw is (3-(-3))/(3-(-3)) = 6/6 = 1.
For points (1,3) and (3,7) the slope is (7-3)/(3-1)=4/2=2

In the slope intercept form, the slope is referenced by 'm'.

y=mx+b

The intercept is the point that the line croses the x axis. It is simply the point on the line when x=0, so it is (0,b). Since the slope defines the rise and fall of the line, if you know one point you can reverse the slope formula to get to a second point. This gives those 'two points' you need to define a line. If you draw the two lines above, you'll find out that the first crosses through 0,0 this the intercept is 0 with a slope of 1...
y=mx+b=1x+0=x, from the points it is hopefully obvious that the equation is correct.

The second line croses the axis at 0,1...making the intercept 1. The resulting equation is y=2x+1.

If you're asking how we derive this form, start with the slope formula...

(Y1-Y2)/(X1-X2)=m.
multiply across the (X1-X2)
(Y1-Y2) = m(X1-X2)
Since the Y intercept is when an X coordinate is 0, let's declare the value of X2 to be 0, this means Y2 is the Y-intercept, that we call 'b'.
Y1 - b = mX1 - 0
Y1 = mX1 + b
which is the standard slope intercept form

not sure this helps...do a search on slope intercept form, there were some interesting sites that came up...

good luck

Answer 2

Well first thing is memorize it y= mx+b the number in front of x is the slope b is the y intercept (the plus or minus) (where it crosses the y axis) To graph plot the y intercept first ex. y=2x+4 slope is 2 y int is 4 go up 4 and put a point. Then use the slope to get the next point. We can write 2 as 2/1, so we take what is on top, the two and go up 2, then over 1 and put a point. Draw a line through.

Answer 3

Clif gave a very good answer. I would add one thing to it.

This is sort of the 'big picture'.

Let's say you are watching a football game on TV. College or NFL, it doesn't matter.

On the screen after every play they show a graphic: "First and ten on the 25", "second and 7 on the 28." "third and 3 on the 32." Like that.

Well those are being written in "football information form" - it's a common, standard way to write what is happening between all those white lines on the field. Everyone uses the same form: {down number} and {yards to go} on the {yardline}

In much the same way, math people use a common way to write what is happening with the lines they work with. They use Clif's version [y] = [mx] + [b]. Kind of {where one dot is} = {where another dot is} + {some goofy math}. It's a form like the football form. Instead of being called "football information form", it's called "slope intercept form".

Use his great math example to work any problems. Now get out there and win this one for your team!

Answer 4

The slope intercept form

is the equation of a straight line in the form

y = mx + b

Where m is the slope of the line and b is the y intercept.

Example

Y = mx + b
Y = 3x + 10

The slope of the line is 3 and the y intercept is 10, where the line crosses the Y axis.