Writing equations in slope-intercept form

nightmarehollow

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Nov 9, 2009
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I am need of help with this. This is my absent work from Friday and I have almost no clue on how to do it.
I know that slope-intercept form is y=mx+b
If someone could explain to me how to write equations in slope-intercept form by getting the numbers from a graph, things would be great.
Thanks to whomever can help!
 
Suppose you have two coordinate points that a line passes through. Let's arbitrarily use (2,3) and (-5,7)

First, find the slope. Difference in y values divided by difference in x values. \(\displaystyle m=\frac{7-3}{-5-2}=\frac{-4}{7}\)

The slope is -4/7. That means it goes down 4 units for every 7 it goes horizontal. Rise over run.

Now, take either coordinate point and the slope and plug them into y=mx+b, then solve for b (where the line crosses the y-axis).

\(\displaystyle 3=\frac{-4}{7}(2)+b\)

\(\displaystyle b=\frac{29}{7}\)

b is the y-intercept.

There it is \(\displaystyle y=\frac{-4}{7}x+\frac{29}{7}\)

That's all there is to it. Try picturing what is going on here. It is just a line. So it can't be too complicated.

On the graph with (0,0) at the origin or center, when x=0, then b=29/7. Then, the line falls -4/7 units for every unit change in x.

See now?. But if you're looking at a graph and it is broken up into a grid, then you can find the slope by just counting the number of little boxes. Go down 4 units and over 7
 
Suppose the graph passes through the points (3,5) and (-2,-5) and we know it is a straight line.
Using the formula y-y[sub:2xagyo2v]1[/sub:2xagyo2v]=m(x-x[sub:2xagyo2v]1[/sub:2xagyo2v]), we first have to find the slope, m. We use the formula m=(y[sub:2xagyo2v]2[/sub:2xagyo2v]-y[sub:2xagyo2v]1[/sub:2xagyo2v])/(x[sub:2xagyo2v]2[/sub:2xagyo2v]-x[sub:2xagyo2v]1[/sub:2xagyo2v]).
m=(-5-5)/(-2-3) getting -10/-5 = 2.
Now we use the first formula...y-y[sub:2xagyo2v]1[/sub:2xagyo2v]=m(x-x[sub:2xagyo2v]1[/sub:2xagyo2v]) and substitute in the values getting
y-(5)=2(x-3) rearrange into the desired form.
y-(5)=2(x-3)
y-5 = 2x-6
y=2x-1 and there it is.
 
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