Graph y-3=-2/3(x+6)

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

Step 1

Move all terms not containing $y$ to the right side of the equation.

Add $3$ to both sides of the equation.

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

Add $- 4$ and $3$ .

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

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.

$y = m x + b$

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

Reorder terms.

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

Remove parentheses.

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

Step 3

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

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

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

$b = - 1$

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

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

y-intercept: $(0, - 1)$

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

y-intercept: $(0, - 1)$

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 terms.

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

Remove parentheses.

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

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

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

Step 5

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

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

y-intercept: $(0, - 1)$

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

Step 6