(-3,5) (-2,-6)

Question

I do not understand equation of a line

Answer 1

You need to understand the concept of the slope of a line. It says how fast y changes as x changes by 1.

That is, if the slope is 3, y increases by 3 whenever x increases by 1. If the slope is -2, y decreases by 2 when x increases by 1.

So, given two points, the slope is the change in y divided by the change in x, as you move from one point to the other. in this case, the slope is

(-6-5)/(-2-(-3)) = -11/1 = -11

That means that y will drop by 11 for every increase of 1 in x.

So, take any point (x,y) on the line. The amount y moves from 5 as x moves away from -3 will be -11 times as much as x's change. So,

y-5 = -11(x-(-3))
y-5 = -11(x+3)
This is called the point-slope form of a line. Technically, we should have used the two-point form of the equation, which would be

(y-5)/(x+3) = (-6-5)/(-2-(-3))

but that is always messy. Much easier to figure the slope first and then just use it. The two-point form says explicitly that the ratio of the changes in y and x is always the same, namely the slope of the line.

The other common form of the equation is slope-intercept: y = mx+b

y-5 = -11(x+3)
y-5 = -11x-33
y = -11x - 28

This makes it easy to find the y-intercept if that'what you want.