What is the equation of a line that passes through (2,-1) and (5,4). Write the equation in general form. Thanks!!!?

Let's start with point slope form of the equation:

y - k = m(x - h)

So first we need the slope, which is the difference in the "y"s over the differences in the "x"s:

(-1 - 4) / (2 - 5)
-5 / (-3)
5/3

So that's your slope, m. Pick a point and use the values to fill in (h, k). I'll use the first point, so now we have:

y + 1 = (5/3)(x - 2)

Now we want it in general form, which is:

ax + by = c

Where b and c are integers and a is a positive integer. So I'll start with multiplying both halves by 3 (the denominator of the slope) and then simplifying:

3y + 3 = 5(x - 2)
3y + 3 = 5x - 10
-5x + 3y = -13

Since we want the coefficient of "x" to be positive, multiply both halves by -1:

5x - 3y = 13

That's the answer to your question. Best Answer if this helped.

The equation of the line :
(y + 1) / (x - 2) = (4 + 1) / (5 - 2)
(y + 1) / (x - 2) = 5 / 3
5(x - 2) = 3(y + 1)
5x - 10 = 3y + 3
5x - 3y - 13 = 0

m = 5 / 3
y - 4 = (5/3) (x - 5)
y = (5/3) x - 25/3 + 12/3
y = (5/3) x - 13/3