Graph y+3x=6

$y + 3 x = 6$

Step 1

Subtract $3 x$ from both sides of the equation.

$y = 6 - 3 x$

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 $- 3 x$ .

$y = - 3 x + 6$

Step 3

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

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

$m = - 3$

$b = 6$

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

Slope: $- 3$

y-intercept: $(0, 6)$

Slope: $- 3$

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.

Reorder $6$ and $- 3 x$ .

$y = - 3 x + 6$

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

$\begin{array}{c} x & y \\ 0 & 6 \\ 1 & 3 \end{array}$

Step 5

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

Slope: $- 3$

y-intercept: $(0, 6)$

$\begin{array}{c} x & y \\ 0 & 6 \\ 1 & 3 \end{array}$

Step 6