Find the Slope and y-intercept -12x-4y=7

$- 12 x - 4 y = 7$

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.

$y = m x + b$

Add $12 x$ to both sides of the equation.

$- 4 y = 7 + 12 x$

Divide each term in $- 4 y = 7 + 12 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 7 + 12 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{7}{- 4} + \frac{12 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{7}{- 4} + \frac{12 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{7}{- 4} + \frac{12 x}{- 4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{7}{4} + \frac{12 x}{- 4}$

Cancel the common factor of $12$ and $- 4$ .

Factor $4$ out of $12 x$ .

$y = - \frac{7}{4} + \frac{4 (3 x)}{- 4}$

Move the negative one from the denominator of $\frac{3 x}{- 1}$ .

$y = - \frac{7}{4} - 1 \cdot (3 x)$

Rewrite $- 1 \cdot (3 x)$ as $- (3 x)$ .

$y = - \frac{7}{4} - (3 x)$

Multiply $3$ by $- 1$ .

$y = - \frac{7}{4} - 3 x$

Reorder $- \frac{7}{4}$ and $- 3 x$ .

$y = - 3 x - \frac{7}{4}$

Step 2

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

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

$m = - 3$

$b = - \frac{7}{4}$

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

Slope: $- 3$

y-intercept: $(0, - \frac{7}{4})$

Slope: $- 3$

y-intercept: $(0, - \frac{7}{4})$

Step 3