Graph graph -27x+18y=54

graph $- 27 x + 18 y = 54$

Solve for $y$ .

Add $27 x$ to both sides of the equation.

$18 y = 54 + 27 x$

Divide each term in $18 y = 54 + 27 x$ by $18$ and simplify.

Divide each term in $18 y = 54 + 27 x$ by $18$ .

$\frac{18 y}{18} = \frac{54}{18} + \frac{27 x}{18}$

Simplify the left side.

Cancel the common factor of $18$ .

Cancel the common factor.

$\frac{18 y}{18} = \frac{54}{18} + \frac{27 x}{18}$

Divide $y$ by $1$ .

$y = \frac{54}{18} + \frac{27 x}{18}$

Simplify the right side.

Simplify each term.

Divide $54$ by $18$ .

$y = 3 + \frac{27 x}{18}$

Cancel the common factor of $27$ and $18$ .

Factor $9$ out of $27 x$ .

$y = 3 + \frac{9 (3 x)}{18}$

Cancel the common factors.

Factor $9$ out of $18$ .

$y = 3 + \frac{9 (3 x)}{9 (2)}$

Cancel the common factor.

$y = 3 + \frac{9 (3 x)}{9 \cdot 2}$

Rewrite the expression.

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

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 $3$ and $\frac{3 x}{2}$ .

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

Reorder terms.

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

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

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

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

$b = 3$

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: $(0, 3)$

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

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.

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

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

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

Reorder terms.

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

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

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

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

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

y-intercept: $(0, 3)$

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

Graph graph -27x+18y=54

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