Graph y=-2/3x+3

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

Step 1

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.

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

Remove parentheses.

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

Step 2

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

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

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

$b = 3$

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: $(0, 3)$

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

y-intercept: $(0, 3)$

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.

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

Reorder terms.

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

Remove parentheses.

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

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

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

Step 4

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

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

y-intercept: $(0, 3)$

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

Step 5