Algebra Examples

$(y + 6) = - \frac{3}{2} (x - 8)$

Step 1

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

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Step 1.1

Subtract $6$ from both sides of the equation.

$y = - \frac{3 x}{2} + 12 - 6$

Step 1.2

Subtract $6$ from $12$ .

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

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

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

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Step 2.2.1

Reorder terms.

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

Step 2.2.2

Remove parentheses.

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

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

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

$b = 6$

Step 3.2

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

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

y-intercept: $(0, 6)$

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

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.

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Step 4.1

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

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Step 4.1.1

Reorder terms.

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

Step 4.1.2

Remove parentheses.

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

Step 4.2

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

$\begin{array}{c} x & y \\ 0 & 6 \\ 2 & 3 \end{array}$

Step 5

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

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

y-intercept: $(0, 6)$

$\begin{array}{c} x & y \\ 0 & 6 \\ 2 & 3 \end{array}$

Step 6