Hi Anthony!
To write an equation for a line given two points, you can:
1. Find the slope.
2. Use the slope and a given point to write the equation in pointslope form.
3. Solve for slopeintercept form if that is necessary.
Here's how you do it for this problem:
1. Find the slope using slope formula ("rise over run"):
m = rise/run = (y_{2}  y_{1})/(x_{2}  x_{1})
For this problem:
(x_{1}, y_{1}) = (3,5)
(x_{2}, y_{2}) = (2,6)
Plug those values into slope formula:
m = (6  5)/(2  (3))
Watch your signs and simplify:
m = (11)/(1) = 11
So, your slope is 11.
2. Now, you can write the line equation in pointslope form,
which looks like this:
y  y_{1} = m(x  x_{1})
Plug in the slope you found, and one of the given points. I'll use (3,5), but you can use either.
y  5 = 11(x  (3))
y  5 = 11(x + 3)
That is the equation in pointslope form.
3. You can then simplify to slopeintercept form, y = mx + b.
Use the pointslope form, and solve for y ("get y alone on one side of the equals sign"):
y  5 = 11(x + 3)
y  5 = 11x  33
y = 11x  33 + 5
y = 11x  28
In slopeintercept form, your answer is:
y = 11x  28
Hope this helps!
1/17/2014

Brittany H.