Algebra Examples

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

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

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Write in

y = m x + b

$y = m x + b$ form.

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Step 1.2.1

Reorder terms.

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

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

Step 1.2.2

Remove parentheses.

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

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

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

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

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

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

Step 2

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

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Step 2.1

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = - \frac{3}{2}

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

b = - 2

$b = - 2$

Step 2.2

The slope of the line is the value of

m

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

b

$b$ .

Slope:

- \frac{3}{2}

$- \frac{3}{2}$

y-intercept:

(0, - 2)

$(0, - 2)$

Slope:

- \frac{3}{2}

$- \frac{3}{2}$

y-intercept:

(0, - 2)

$(0, - 2)$

Step 3

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 3.1

Write in

y = m x + b

$y = m x + b$ form.

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Step 3.1.1

Reorder terms.

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

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

Step 3.1.2

Remove parentheses.

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

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

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

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

Step 3.2

Create a table of the

x

$x$ and

y

$y$ values.

\begin{matrix} x & y 0 & - 2 2 & - 5 \end{matrix}

$\begin{array}{c} x & y \\ 0 & - 2 \\ 2 & - 5 \end{array}$

\begin{matrix} x & y 0 & - 2 2 & - 5 \end{matrix}

$\begin{array}{c} x & y \\ 0 & - 2 \\ 2 & - 5 \end{array}$

Step 4

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

Slope:

- \frac{3}{2}

$- \frac{3}{2}$

y-intercept:

(0, - 2)

$(0, - 2)$

\begin{matrix} x & y 0 & - 2 2 & - 5 \end{matrix}

$\begin{array}{c} x & y \\ 0 & - 2 \\ 2 & - 5 \end{array}$

Step 5