Algebra Examples

3 x + y = - 6

$3 x + y = - 6$

Step 1

Subtract

3 x

$3 x$ from both sides of the equation.

y = - 6 - 3 x

$y = - 6 - 3 x$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.2

Reorder

- 6

$- 6$ and

- 3 x

$- 3 x$ .

y = - 3 x - 6

$y = - 3 x - 6$

y = - 3 x - 6

$y = - 3 x - 6$

Step 3

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

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Step 3.1

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = - 3

$m = - 3$

b = - 6

$b = - 6$

Step 3.2

The slope of the line is the value of

m

$m$ , and the y-intercept is the value of

b

$b$ .

Slope:

- 3

$- 3$

y-intercept:

(0, - 6)

$(0, - 6)$

Slope:

- 3

$- 3$

y-intercept:

(0, - 6)

$(0, - 6)$

Step 4

Any line can be graphed using two points. Select two

x

$x$ values, and plug them into the equation to find the corresponding

y

$y$ values.

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Step 4.1

Reorder

- 6

$- 6$ and

- 3 x

$- 3 x$ .

y = - 3 x - 6

$y = - 3 x - 6$

Step 4.2

Create a table of the

x

$x$ and

y

$y$ values.

\begin{matrix} x & y 0 & - 6 1 & - 9 \end{matrix}

$\begin{array}{c} x & y \\ 0 & - 6 \\ 1 & - 9 \end{array}$

\begin{matrix} x & y 0 & - 6 1 & - 9 \end{matrix}

$\begin{array}{c} x & y \\ 0 & - 6 \\ 1 & - 9 \end{array}$

Step 5

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

Slope:

$- 3$

y-intercept:

$(0, - 6)$

$\begin{array}{c} x & y \\ 0 & - 6 \\ 1 & - 9 \end{array}$

Step 6

$3 x + y = - 6$

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