Question

I do not understand point-slope and standard form. Please help me.

Answer 1

The point-slope form relies on the fact that the slope of a line is constant. How is the slope determined? It's the change in y divided by the change in x.

So, if you have a slope = m, then if you pick any point P:(h,k), then for any other point (x,y) on the line, the change in y: (y-k) divided by the change in x: (x-h) never changes. It's m.

For example, if you have a point (3,6) and a slope -2, then for any point (x,y) on the line,

(y-6)/(x-3) = -2
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Now the standard form is

ax + by + c = 0

If you plug in x=0 you get by+c = 0
If you plug in y=0 you get ax+c = 0

This will provide the two intercepts, and you can easily draw the line.

For example, if

2x - 5y + 7 = 0

The x-intercept is at (-7/2, 0)
The y-intercept is at (0, 7/5)

Not quite sure what else you don't get about the standard form. There are lots of ways to look at it.