find the equation of the line that passes thru the point p(5,-1) and (10,-6) use info y-y1 over x-x1?

Answer 1

When a line passes through points (x1, y1) and (x2, y2), It can be written in the form:
y = mx + c ..... (1)

where m = (y2 - y1)/(x2 - x1)

We can find c and with that the equation.

Here, m = (-6 + 1)/(10 - 5) = -5/5 = -1

Using (1), we get,

y = -x + c ..... (2)
(5, -1) is a solution of the equation, so put x = 5 and y = -1 in the equation (2) to get c,

-1 = -5 + c
c = 4

We have our equation,
y = 4 - x
-----> x + y = 4

DONE

Answer 2

The y-y1 over x-x1 is the slope of the line. Remember the equation of a line is y=mx+b where m is the slope and b is the y-intercept. Calculate the slope first. Let's use (5,-1) as (x1 ,y1). m = [-6-(-1)]/[10-5] = -5/5 = -1. Now, put this in for m into your equation. y = -1x+b. Choose one of the points you started with to plug in for x and y, and solve for b.

I'll use (5,-1): -1=-1*(5)+b
-1=-5+b
4=b

Now you just have to plug in:
y=-1x+4 (or, you can get rid of the 1 to have y = -x+4)

Answer 3

y= 4 - x