Find the y-intercept 7x-19y=209

$7 x - 19 y = 209$

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 $7 x$ from both sides of the equation.

$- 19 y = 209 - 7 x$

Divide each term in $- 19 y = 209 - 7 x$ by $- 19$ and simplify.

Divide each term in $- 19 y = 209 - 7 x$ by $- 19$ .

$\frac{- 19 y}{- 19} = \frac{209}{- 19} + \frac{- 7 x}{- 19}$

Simplify the left side.

Cancel the common factor of $- 19$ .

Cancel the common factor.

$\frac{- 19 y}{- 19} = \frac{209}{- 19} + \frac{- 7 x}{- 19}$

Divide $y$ by $1$ .

$y = \frac{209}{- 19} + \frac{- 7 x}{- 19}$

Simplify the right side.

Simplify each term.

Divide $209$ by $- 19$ .

$y = - 11 + \frac{- 7 x}{- 19}$

Dividing two negative values results in a positive value.

$y = - 11 + \frac{7 x}{19}$

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

Reorder $- 11$ and $\frac{7 x}{19}$ .

$y = \frac{7 x}{19} - 11$

Reorder terms.

$y = \frac{7}{19} x - 11$

Step 2

Using the slope-intercept form, the y-intercept is $- 11$ .

$b = - 11$

Step 3

y-intercept in point form.

$(0, - 11)$

Step 4