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pre algebra

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write an equation for the line through the given points or through the given point with the given slope

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"
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

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