Graph 6x-4y=24

$6 x - 4 y = 24$

Step 1

Solve for $y$ .

Subtract $6 x$ from both sides of the equation.

$- 4 y = 24 - 6 x$

Divide each term in $- 4 y = 24 - 6 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 24 - 6 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{24}{- 4} + \frac{- 6 x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{24}{- 4} + \frac{- 6 x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{24}{- 4} + \frac{- 6 x}{- 4}$

Simplify the right side.

Simplify each term.

Divide $24$ by $- 4$ .

$y = - 6 + \frac{- 6 x}{- 4}$

Cancel the common factor of $- 6$ and $- 4$ .

Factor $- 2$ out of $- 6 x$ .

$y = - 6 + \frac{- 2 (3 x)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$y = - 6 + \frac{- 2 (3 x)}{- 2 (2)}$

Cancel the common factor.

$y = - 6 + \frac{- 2 (3 x)}{- 2 \cdot 2}$

Rewrite the expression.

$y = - 6 + \frac{3 x}{2}$

Step 2

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.

$y = m x + b$

Reorder $- 6$ and $\frac{3 x}{2}$ .

$y = \frac{3 x}{2} - 6$

Reorder terms.

$y = \frac{3}{2} x - 6$

Step 3

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

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

$m = \frac{3}{2}$

$b = - 6$

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

Slope: $\frac{3}{2}$

y-intercept: $(0, - 6)$

Slope: $\frac{3}{2}$

y-intercept: $(0, - 6)$

Step 4

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

Write in $y = m x + b$ form.

Reorder $- 6$ and $\frac{3 x}{2}$ .

$y = \frac{3 x}{2} - 6$

Reorder terms.

$y = \frac{3}{2} x - 6$

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

$\begin{array}{c} x & y \\ 0 & - 6 \\ 2 & - 3 \end{array}$

Step 5

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

Slope: $\frac{3}{2}$

y-intercept: $(0, - 6)$

$\begin{array}{c} x & y \\ 0 & - 6 \\ 2 & - 3 \end{array}$

Step 6

Graph 6x-4y=24

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