Find the equation in slope-intercept form of the line through points (-2, 5) and (6, -15).
How would i do this? Do i use y = mx+b? or what im not sure how to do it
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There are 3 main formulas.. it helps to remember them, you'll keep running into them if you keep doing math all the way through to calculus.
Slope intercept is y=mx+b
Point Slope y-y1=m(x-x1)
Slope m =(y1-y2)/(x1-x2) = (rise/run) = a difference between two points on the rise)/(a difference between two points in the run)
This idea of differences between two points is going to keep repeating itself over and over again. And the the idea of the triangles that rise/run creates and the ratio and Tan of these relationships. So try to get a good visual idea of that relationship as you practice this stuff, and all this math is going to get intuitive and a lot easier.
Think of Slope Intercept as the one that anchors itself on the y-intercept.. The value for b is going to be the actual y-intercept.
But because you can't know this value for the y-intercept from that information, you need to use the other equations here, and convert them into slope intercept.
1. Use Slope formula to work out a value for m, by converting the two points into rise/run.
2. Plug that value for m into your point slope formula then solve for y when x=0
3. This will give you a value for b that you can now plug into your slope intercept formula.
(-2,5) and (6, -15)
First find slope. (m) (y2-y1)/(x2-x1) x2 -x1 = 6 - (-2) so it becomes 6 + 2
m=-20/8 is the slope
now replace x and y terms (y = mx+b)
80/8=b the y intercept
Thus equation being
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the 2nd stage you plug the values into the point slope equation .. so
you can use either point for point slope.. so (-2,5) into
y-y1 = m(x-x1)
which you can convert quickly into a very similar equation to point slope.
y = m(x-x1) + y1
So next we solve for y with x=0 so the equation becomes..
y = m(0-x1)+ y1
x1 = -2
y1 = 5
Using slope equation plug in your points
m = y1 - y2 / x1 - x2
m = 5-(-15) / -2 - 6
Using point slope, Solve for y when x =0
y - y1 = m(x-x1)
y = m(x-x1)+y1 rearrange it
x = 0
substitute and simplify
y = (-5/2)(0-(-2)+5
y = (-5/2)(0+2)+5
y = (-5/2)(2)+5
y = (-10/2)+5
y = (-5/1)+5
y = -5+5
y = 0
From here you just take the slope intercept formula y=mx+b and plug in your values for m and b
You know m from the slope formula result
Slope intercept gets it's name because it describes the line from where x=0, at the y-intercept. Note that at this point y=b, and so now you now the value for b too.