Find the Slope and y-intercept 8x+12y=9

$8 x + 12 y = 9$

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 $8 x$ from both sides of the equation.

$12 y = 9 - 8 x$

Divide each term in $12 y = 9 - 8 x$ by $12$ and simplify.

Divide each term in $12 y = 9 - 8 x$ by $12$ .

$\frac{12 y}{12} = \frac{9}{12} + \frac{- 8 x}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 y}{12} = \frac{9}{12} + \frac{- 8 x}{12}$

Divide $y$ by $1$ .

$y = \frac{9}{12} + \frac{- 8 x}{12}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $9$ and $12$ .

Factor $3$ out of $9$ .

$y = \frac{3 (3)}{12} + \frac{- 8 x}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

$y = \frac{3 \cdot 3}{3 \cdot 4} + \frac{- 8 x}{12}$

Cancel the common factor.

$y = \frac{3 \cdot 3}{3 \cdot 4} + \frac{- 8 x}{12}$

Rewrite the expression.

$y = \frac{3}{4} + \frac{- 8 x}{12}$

Cancel the common factor of $- 8$ and $12$ .

Factor $4$ out of $- 8 x$ .

$y = \frac{3}{4} + \frac{4 (- 2 x)}{12}$

Cancel the common factors.

Factor $4$ out of $12$ .

$y = \frac{3}{4} + \frac{4 (- 2 x)}{4 (3)}$

Cancel the common factor.

$y = \frac{3}{4} + \frac{4 (- 2 x)}{4 \cdot 3}$

Rewrite the expression.

$y = \frac{3}{4} + \frac{- 2 x}{3}$

Move the negative in front of the fraction.

$y = \frac{3}{4} - \frac{2 x}{3}$

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

Reorder $\frac{3}{4}$ and $- \frac{2 x}{3}$ .

$y = - \frac{2 x}{3} + \frac{3}{4}$

Reorder terms.

$y = - (\frac{2}{3} x) + \frac{3}{4}$

Remove parentheses.

$y = - \frac{2}{3} x + \frac{3}{4}$

Step 2

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

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

$m = - \frac{2}{3}$

$b = \frac{3}{4}$

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, \frac{3}{4})$

Slope: $- \frac{2}{3}$

y-intercept: $(0, \frac{3}{4})$

Step 3

Find the Slope and y-intercept 8x+12y=9

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