Question

write an equation for the line through the given points or through the given point with the given slope
(5,7),(6,8)
(1,2),(3,8)
(0,5),(-3,2)
(8,11),(6,16)

For each of them, use the standard formula
(y- y1) = [(y2-y1)/x2-x1)]*(x-x1)
In the first case, that gives you
(y-7) = (1/1)* (x-5)
y = x+2

drwls, thanks for the help. I was trying to check my sons answers. He got the first one right. When he is doing this homework he is not sure of what he is doing. I showed him this and asked if he understood the standard formula and he looked like a deer in headlights! I said to make the graph and maybe that would help. Any other help. Thanks

In the "standard formula"
[(y2-y1)/(x2-x1)]
is the slope of the line, usually called "m".

The standard formula is just is a mathematical statement that the change in y from a point (x1,y1) is equal to the slope, multiplied by the change in x measured from the same point. Some texts may use a different approach, but I find the one that I wrote easiest to remember.

Applying the same method to the second problem,
y -2 = (6/2) (x-1)
y = 2 + 3x -3
y = 3x - 1