Question

How do you write `2x - 3y > 7` in slope intercept form?

Answer 1

The boundary can be written in slope-intercept form giving
`color(white)("XXXX")` `y < 2/3x+(-7/3)`

Explanation:

given `2x-3y > 7`

adding `3y` to both sides
`color(white)("XXXX")` `2x > 3y+7`

subtracting 7 from both sides
`color(white)("XXXX")` `2x-7 > 3y`

dividing both sides by `3`
`color(white)("XXXX")` `2/3x-7/3 > y`

Reversing the sides
`color(white)("XXXX")` `y < 2/3-7/3`

or (in explicit slope-intercept form
`color(white)("XXXX")` `y < (2/3)x + (-7/3)`
where the boundary line has a slope of `2/3` and a y-intercept of `(-7/3)`