Question

Write the slope-intercept inequality of the line . (0,-1) (6,3)

Answer 1

given that the bottom right corner is shaded

first find the equation of the line

find the line passing through (0,-1) and (6,3)
hey, look, when x=0, y=-1, that's the y intercept
y=mx+b, b=y intercept
so y=mx-1 is the equation
now find m
we are given (6,3)
so x=6 and y=3
subsitute
3=6m-1
add 1 both sides
4=6m
divide by 6 both sides
2/3=m
y=2/3x-1 is the equation
ok, so since it is a solid line, it includes the line so our equation is either

`y \geq (2)/(3)x-1` or
`y \leq (2)/(3)x-1`
find a point on the bottom left
so maybe 1 below any of the given points
(0,-1) is given point so (0,-2) should work
test any of them

`y \geq (2)/(3)x-1`

`-2 \geq (2)/(3)(0)-1`

`-2 \geq 0-1`

`-2 \geq -1`
false
therfor our equation is

`y \leq (2)/(3)x-1`