What is the equation of the line that passes through the points (2,-1) and (5,5)

Answer 1

(x1,y1) = (2, -1)

(x2, y2) = (5,5)

the equation is y-y1 = m(x-x1)

m = (y2-y1)/(x2-x1) = ( 5 +1)/5-2) = 6/3

m = 2

SO, y +1 = 2(x-2)

y+ 1 = 2x - 4

y = 2x -5

Answer 2

The slope (m) is calculated from the slope equation:

So m = (5 - -1)/(5 - 2) = (5 + 1)/(5 - 2) = 6/3 = 2

Using the slope-intercept form of a line (y = mx + b) we cam plug in the "m" and get:

y = 2x + b

The only thing left to do is find "b".

We can use one of the points to find it. You can choose either one, I'll pick (5, 5). It is and (x, y) so x = 5 and y = 5. We can plug those into our equation like this:

5 = 2(5) + b

5 = 10 + b

5 - 10 = b

b = -5

So we can plug that value of "b" into our equation and get:

y = 2x - 5