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

Jul 14, 2015

Slope $= 3$
y intercept is $\frac{1}{3}$

#### Explanation:

Slope
From standard form:
$\textcolor{w h i t e}{\text{XXXX}}$$A x + B y = C$
the slope can be determined as $\left(- \frac{B}{A}\right)$
or
you could convert the given equation into slope intercept form:
$\textcolor{w h i t e}{\text{XXXX}}$$9 x - 3 y = - 1$

$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow - 3 y = - 9 x - 1$

$\textcolor{w h i t e}{\text{XXXX}}$$= y = 3 x + \frac{1}{3}$
$\textcolor{w h i t e}{\text{XXXX}}$$\textcolor{w h i t e}{\text{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 $\frac{1}{3}$).

If you used the slope $= \left(- \frac{B}{A}\right)$ version
set $x = 0$ in the given equation and solve for $y$
$\textcolor{w h i t e}{\text{XXXX}}$$9 \left(0\right) - 3 y = - 1$

$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow - 3 y = - 1$

$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow y = \frac{1}{3}$