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.

$y = m x + b$

Subtract $12 x$ from 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.

Dividing two negative values results in a positive value.

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

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

Factor $- 4$ out of $- 12 x$ .

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

Cancel the common factors.

Factor $- 4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{7}{4} + \frac{3 x}{1}$

Divide $3 x$ 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