Graph 27+3y=6x

$27 + 3 y = 6 x$

Solve for $y$ .

Subtract $27$ from both sides of the equation.

$3 y = 6 x - 27$

Divide each term in $3 y = 6 x - 27$ by $3$ and simplify.

Divide each term in $3 y = 6 x - 27$ by $3$ .

$\frac{3 y}{3} = \frac{6 x}{3} + \frac{- 27}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6 x}{3} + \frac{- 27}{3}$

Divide $y$ by $1$ .

$y = \frac{6 x}{3} + \frac{- 27}{3}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 x$ .

$y = \frac{3 (2 x)}{3} + \frac{- 27}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = \frac{3 (2 x)}{3 (1)} + \frac{- 27}{3}$

Cancel the common factor.

$y = \frac{3 (2 x)}{3 \cdot 1} + \frac{- 27}{3}$

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{- 27}{3}$

Divide $2 x$ by $1$ .

$y = 2 x + \frac{- 27}{3}$

Divide $- 27$ by $3$ .

$y = 2 x - 9$

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 $y = m x + b$ .

$m = 2$

$b = - 9$

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

Slope: $2$

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

Slope: $2$

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

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.

$\begin{array}{c} x & y \\ 0 & - 9 \\ 1 & - 7 \end{array}$

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

Slope: $2$

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

$\begin{array}{c} x & y \\ 0 & - 9 \\ 1 & - 7 \end{array}$

Graph 27+3y=6x

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