Graph -12x-3y=9

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Trigonometry

Graph -12x-3y=9

$- 12 x - 3 y = 9$

Solve for $y$ .

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

$- 3 y = 9 + 12 x$

Divide each term by $- 3$ and simplify.

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Divide each term in $- 3 y = 9 + 12 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{9}{- 3} + \frac{12 x}{- 3}$

Cancel the common factor of $- 3$ .

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Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{9}{- 3} + \frac{12 x}{- 3}$

Divide $y$ by $1$ .

$y = \frac{9}{- 3} + \frac{12 x}{- 3}$

Simplify each term.

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Divide $9$ by $- 3$ .

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

Cancel the common factor of $12$ and $- 3$ .

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Factor $3$ out of $12 x$ .

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

Move the negative one from the denominator of $\frac{4 x}{- 1}$ .

$y = - 3 - 1 \cdot (4 x)$

Rewrite $- 1 \cdot (4 x)$ as $- (4 x)$ .

$y = - 3 - (4 x)$

Multiply $4$ by $- 1$ .

$y = - 3 - 4 x$

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.

$y = m x + b$

Reorder $- 3$ and $- 4 x$ .

$y = - 4 x - 3$

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 $y = m x + b$ .

$m = - 4$

$b = - 3$

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

Slope: $- 4$

y-intercept: $(0, - 3)$

Slope: $- 4$

y-intercept: $(0, - 3)$

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Find the x-intercept.

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To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = - 3 - 4 x$

Solve the equation.

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Rewrite the equation as $- 3 - 4 x = 0$ .

$- 3 - 4 x = 0$

Add $3$ to both sides of the equation.

$- 4 x = 3$

Divide each term by $- 4$ and simplify.

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

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

Cancel the common factor of $- 4$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Move the negative in front of the fraction.

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

x-intercept(s) in point form.

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

Find the y-intercept.

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To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = - 3 - 4 \cdot 0$

Solve the equation.

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Remove parentheses.

$y = - 3 - 4 \cdot 0$

Simplify $- 3 - 4 \cdot 0$ .

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Multiply $- 4$ by $0$ .

$y = - 3 + 0$

Add $- 3$ and $0$ .

$y = - 3$

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ - \frac{3}{4} & 0 \\ 0 & - 3 \end{array}$

Graph the line using the slope and the y-intercept, or the points.

Slope: $- 4$

y-intercept: $(0, - 3)$

$\begin{array}{c} x & y \\ - \frac{3}{4} & 0 \\ 0 & - 3 \end{array}$

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