Question

How would you write an equation of the line with the points (-2,4) (4,1)

Answer 1

There are several eqaiton types

1. point slope
passes through (x1,y1) and has a slope of m
y-y1=m(x-x1)

2. slope intercept
y=mx+b
m=slope
b=y intercept

3. standard form
ax+by=c or ax+by-c=0
where a, b, and c are integers and a is usually positive


so


first find the slope

slope between (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)
slope between (-2,4) and (4,1) is (1-4)/(4-(-2))=(-3)/(4+2)=-3/6=-1/2

use point slope
using point (4,1)
y-1=-1/2(x-4)

now let's do slope intercept
solve for y
y-1=-1/2(x-4)
y-1=-1/2x+2
y=-1/2x+3 is slope intercept

now standard form
times both sides by 2
2y=-x+6
add x both sides
x+2y=6 is standard form



so

possible equations are
$y-1=\frac{-1}{2}(x-4)$
$y-4=\frac{-1}{2}(x+2)$
$y=\frac{-1}{2}x+3$
x+2y=6
x+2y-6=0