Find the y-intercept 2y+6=5x

$2 y + 6 = 5 x$

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 $6$ from both sides of the equation.

$2 y = 5 x - 6$

Divide each term in $2 y = 5 x - 6$ by $2$ and simplify.

Divide each term in $2 y = 5 x - 6$ by $2$ .

$\frac{2 y}{2} = \frac{5 x}{2} + \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{5 x}{2} + \frac{- 6}{2}$

Divide $y$ by $1$ .

$y = \frac{5 x}{2} + \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$y = \frac{5 x}{2} - 3$

Reorder terms.

$y = \frac{5}{2} x - 3$

Step 2

Using the slope-intercept form, the y-intercept is $- 3$ .

$b = - 3$

Step 3

y-intercept in point form.

$(0, - 3)$

Step 4