Find the y-intercept 10x+9y=45

$10 x + 9 y = 45$

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 $10 x$ from both sides of the equation.

$9 y = 45 - 10 x$

Divide each term in $9 y = 45 - 10 x$ by $9$ and simplify.

Divide each term in $9 y = 45 - 10 x$ by $9$ .

$\frac{9 y}{9} = \frac{45}{9} + \frac{- 10 x}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{45}{9} + \frac{- 10 x}{9}$

Divide $y$ by $1$ .

$y = \frac{45}{9} + \frac{- 10 x}{9}$

Simplify the right side.

Simplify each term.

Divide $45$ by $9$ .

$y = 5 + \frac{- 10 x}{9}$

Move the negative in front of the fraction.

$y = 5 - \frac{10 x}{9}$

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

Reorder $5$ and $- \frac{10 x}{9}$ .

$y = - \frac{10 x}{9} + 5$

Reorder terms.

$y = - (\frac{10}{9} x) + 5$

Remove parentheses.

$y = - \frac{10}{9} x + 5$

Step 2

Using the slope-intercept form, the y-intercept is $5$ .

$b = 5$

Step 3

y-intercept in point form.

$(0, 5)$

Step 4