Graph -1/3y+4x=3

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

Step 1

Solve for $y$ .

Subtract $4 x$ from both sides of the equation.

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

Multiply both sides of the equation by $- 3$ .

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 3 (- \frac{y}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{y}{3}$ into the numerator.

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

$- - y = - 3 (3 - 4 x)$

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $y$ by $1$ .

$y = - 3 (3 - 4 x)$

Simplify the right side.

Simplify $- 3 (3 - 4 x)$ .

Apply the distributive property.

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

Multiply.

Multiply $- 3$ by $3$ .

$y = - 9 - 3 (- 4 x)$

Multiply $- 4$ by $- 3$ .

$y = - 9 + 12 x$

Reorder $- 9$ and $12 x$ .

$y = 12 x - 9$

Step 2

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

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

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

$m = 12$

$b = - 9$

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

Slope: $12$

y-intercept: $(0, - 9)$

Slope: $12$

y-intercept: $(0, - 9)$

Step 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.

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

$\begin{array}{c} x & y \\ 0 & - 9 \\ 1 & 3 \end{array}$

Step 4

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

Slope: $12$

y-intercept: $(0, - 9)$

$\begin{array}{c} x & y \\ 0 & - 9 \\ 1 & 3 \end{array}$

Step 5

Graph -1/3y+4x=3

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