Find the Slope and y-intercept 12x=2y+1

$12 x = 2 y + 1$

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.

$y = m x + b$

Rewrite the equation as $2 y + 1 = 12 x$ .

$2 y + 1 = 12 x$

Subtract $1$ from both sides of the equation.

$2 y = 12 x - 1$

Divide each term in $2 y = 12 x - 1$ by $2$ and simplify.

Divide each term in $2 y = 12 x - 1$ by $2$ .

$\frac{2 y}{2} = \frac{12 x}{2} + \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{12 x}{2} + \frac{- 1}{2}$

Divide $y$ by $1$ .

$y = \frac{12 x}{2} + \frac{- 1}{2}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $12$ and $2$ .

Factor $2$ out of $12 x$ .

$y = \frac{2 (6 x)}{2} + \frac{- 1}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$y = \frac{2 (6 x)}{2 (1)} + \frac{- 1}{2}$

Cancel the common factor.

$y = \frac{2 (6 x)}{2 \cdot 1} + \frac{- 1}{2}$

Rewrite the expression.

$y = \frac{6 x}{1} + \frac{- 1}{2}$

Divide $6 x$ by $1$ .

$y = 6 x + \frac{- 1}{2}$

Move the negative in front of the fraction.

$y = 6 x - \frac{1}{2}$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 6$

$b = - \frac{1}{2}$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $6$

y-intercept: $(0, - \frac{1}{2})$

Slope: $6$

y-intercept: $(0, - \frac{1}{2})$

Step 3