Linear Algebra Examples

$6 x + 2 y = - 46$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $6 x$ from both sides of the equation.

$2 y = - 46 - 6 x$

Step 1.2

Divide each term in $2 y = - 46 - 6 x$ by $2$ and simplify.

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Step 1.2.1

Divide each term in $2 y = - 46 - 6 x$ by $2$ .

$\frac{2 y}{2} = \frac{- 46}{2} + \frac{- 6 x}{2}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 46}{2} + \frac{- 6 x}{2}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 46}{2} + \frac{- 6 x}{2}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $- 46$ by $2$ .

$y = - 23 + \frac{- 6 x}{2}$

Step 1.2.3.1.2

Cancel the common factor of $- 6$ and $2$ .

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Step 1.2.3.1.2.1

Factor $2$ out of $- 6 x$ .

$y = - 23 + \frac{2 (- 3 x)}{2}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $2$ out of $2$ .

$y = - 23 + \frac{2 (- 3 x)}{2 (1)}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = - 23 + \frac{2 (- 3 x)}{2 \cdot 1}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = - 23 + \frac{- 3 x}{1}$

Step 1.2.3.1.2.2.4

Divide $- 3 x$ by $1$ .

$y = - 23 - 3 x$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2

Reorder $- 23$ and $- 3 x$ .

$y = - 3 x - 23$

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

$m = - 3$

$b = - 23$

Step 3.2

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

Slope: $- 3$

y-intercept: $(0, - 23)$

Slope: $- 3$

y-intercept: $(0, - 23)$

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.

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Step 4.1

Reorder $- 23$ and $- 3 x$ .

$y = - 3 x - 23$

Step 4.2

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

$\begin{array}{c} x & y \\ 0 & - 23 \\ 1 & - 26 \end{array}$

Step 5

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

Slope: $- 3$

y-intercept: $(0, - 23)$

$\begin{array}{c} x & y \\ 0 & - 23 \\ 1 & - 26 \end{array}$

Step 6