Question

Find the equation of a line passing through (-2,5) and (3,4) in Ax+By=C

Answer 1

First, find the slope,
\[\large \frac{ y_2-y_1 }{ x_2-x_1 }\]
\[\large \frac{ 4-5 }{ 3 + 2 } = -1/5\]
Input your x and y coordinate from one of those to get b.
5 = (-1/5)(-2) + b
5 = 2/5 + b
4 3/5 = b
your resulting equation is.
\[\large y = \frac{ 1 }{ 5 }x +4\frac{ 3 }{ 5 }\]
from there you need to get whole numbers and get x on the other side.

Answer 2

\[\large -\frac{ 1 }{ 5 }x + y = \frac{ 23 }{ 5 }\]
Now you need to multiply the equation by a number so that we get whole numbers.
Let's multiply the equation by 5.
\[\large 5 \times (\frac{ -1 }{ 5 }x + y = \frac{ 23 }{ 5 })\]
you get
\[\large \frac{ -5 }{ 5 }x + 5y = \frac{ 115 }{ 5 }\]
reduce the fractions.
\[\large -x + 5y = 23\]
This is your standard form for your equation.