Question

How do you find the slope and y-intercept given `9x-3y= -1`?

Answer 1

Slope `=3`
y intercept is `1/3`

Explanation:

Slope
From standard form:
`color(white)("XXXX")` `Ax+By = C`
the slope can be determined as `(-B/A)`
or
you could convert the given equation into slope intercept form:
`color(white)("XXXX")` `9x-3y =-1`

`color(white)("XXXX")` `rarr -3y = -9x-1`

`color(white)("XXXX")` `= y = 3x+1/3`
`color(white)("XXXX")` `color(white)("XXXX")`(slope intercept form)

y-intercept
If you used the "convert to slope-intercept form" version (above) then the y-intercept can be read directly from the equation (as `1/3`).

If you used the slope `= (-B/A)` version
set `x=0` in the given equation and solve for `y`
`color(white)("XXXX")` `9(0) - 3y = -1`

`color(white)("XXXX")` `rarr -3y = -1`

`color(white)("XXXX")` `rarr y = 1/3`