How do you figure out slope-intercept form?

Question

I'm in 7th grade (12 yrs old), and I like going above and beyond. So, I got this book, and I went to the graphing section. I know the formula is y=mx+b, but what does each mean?

I already know point to point (change in y over change in x).

Answer 1

The slope-intercept form of an equation makes it very easy to graph the equation.

You say you already understand the rise over the run...that's m in the formula, the number in front of x.

b is the y-intercept. This is the value of y where the line crosses the y-axis, i.e., where x=0.

So, given an equation that looks like y=mx + b, for example

y = 2x + 7

To graph the equation, first you mark the y-intercept, which would be (0, 7) in this case, and then you go up 2 (rise) and to the right 1 (run), and mark the point (1,9), which is (0+1,2+7). Then draw a line through those two points and you're done.

Answer 2

To make it very simple:
the b is where you plot the first point (on the y-axis)
the m is the pattern you follow
ex: y=5x + 10
10 is the first point on the y-axis, and from there you go up 5 units on the y-axis for every one on the x-axis.
If it was y= -5x + 10, there you would decrease 5 y-axis units for every 1 unit on the x-axis
hope this helps

Answer 3

y = mx + b

slope = m
y-intercept =b

any linear function
y or y(x) can be written as mx +b .
here y is directly proportional to x and the propotionality constant is m (signifying rate of change or how y changes with respect to x)and b is the y-intercept or deviation from zero of the graph.actually its a straight line form. obtained by theory of statistics.

Answer 4

If you have two points, (a1,a2) and (b1,b2), find the slope:

m = (a2-b2)/(a1-b1)

Then you have the following

y = mx + b

You know m, and you know two values of x and y. Plug in one of the points as follows:

a2 = ma1 + b

You can use the other point as well. Then solve for b, and you have your equation!