Question

Find the equation, in standard form, of the line passing through the points (5,1) and (-2,3).

Answer 1

use
\[\frac{ y-y _{1} }{ x-x _{1} }=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\]

Answer 2

once you plug in the numbers, what do you do?

Answer 3

try to simplify and get
y=mx+c
where
m=slope
c=y-intercept

Answer 4

you are given 2 points on the line use this to find the slope
the slope is the change in y / corresponding change in x
m = (y2 -y1) / (x2 -x1)
once you have the slope use one of the points to find the y-intercept, b
now you have m and b you can write the general equation.

for this problem you have (5,1) and (-2, 3)
the slope ,m = 3-1/-2-5 = 2/-7
using (3, -2)
3 = -2/7(-2) + b
b = 3-4/7 =(21-4)/7
y = -2/7(x) + 17/7
multiply everything by 7
and rewrite to the form ax + by = c

Answer 5

2x + 7y = 17