Find the y-intercept 6x-12y=192

$6 x - 12 y = 192$

Step 1

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Subtract $6 x$ from both sides of the equation.

$- 12 y = 192 - 6 x$

Divide each term in $- 12 y = 192 - 6 x$ by $- 12$ and simplify.

Divide each term in $- 12 y = 192 - 6 x$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{192}{- 12} + \frac{- 6 x}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{192}{- 12} + \frac{- 6 x}{- 12}$

Divide $y$ by $1$ .

$y = \frac{192}{- 12} + \frac{- 6 x}{- 12}$

Simplify the right side.

Simplify each term.

Divide $192$ by $- 12$ .

$y = - 16 + \frac{- 6 x}{- 12}$

Cancel the common factor of $- 6$ and $- 12$ .

Factor $- 6$ out of $- 6 x$ .

$y = - 16 + \frac{- 6 (x)}{- 12}$

Cancel the common factors.

Factor $- 6$ out of $- 12$ .

$y = - 16 + \frac{- 6 (x)}{- 6 (2)}$

Cancel the common factor.

$y = - 16 + \frac{- 6 x}{- 6 \cdot 2}$

Rewrite the expression.

$y = - 16 + \frac{x}{2}$

Write in $y = m x + b$ form.

Reorder $- 16$ and $\frac{x}{2}$ .

$y = \frac{x}{2} - 16$

Reorder terms.

$y = \frac{1}{2} x - 16$

Step 2

Using the slope-intercept form, the y-intercept is $- 16$ .

$b = - 16$

Step 3

y-intercept in point form.

$(0, - 16)$

Step 4