Find the Slope and Y-Intercept 3x-4y=12

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Algebra

$3 x - 4 y = 12$

Rewrite in slope-intercept form.

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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 $3 x$ from both sides of the equation.

$- 4 y = 12 - 3 x$

Divide each term by $- 4$ and simplify.

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Divide each term in $- 4 y = 12 - 3 x$ by $- 4$ .

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

Cancel the common factor of $- 4$ .

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Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify $\frac{12}{- 4} + \frac{- 3 x}{- 4}$ .

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Simplify each term.

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Divide $12$ by $- 4$ .

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

Dividing two negative values results in a positive value.

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

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

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

Rewrite in slope-intercept form.

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

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

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

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

$b = - 3$

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

Slope: $\frac{3}{4}$

y-intercept: $- 3$

Slope: $\frac{3}{4}$

y-intercept: $- 3$

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