Pre-Algebra Examples

$y = \frac{- 10 - 4 x}{10}$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Simplify $- \frac{5 + 2 x}{5}$ .

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Step 1.2.1

Split the fraction $\frac{5 + 2 x}{5}$ into two fractions.

$y = - (\frac{5}{5} + \frac{2 x}{5})$

Step 1.2.2

Divide $5$ by $5$ .

$y = - (1 + \frac{2 x}{5})$

Step 1.2.3

Apply the distributive property.

$y = - 1 \cdot 1 - \frac{2 x}{5}$

Step 1.2.4

Simplify the expression.

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Step 1.2.4.1

Multiply $- 1$ by $1$ .

$y = - 1 - \frac{2 x}{5}$

Step 1.2.4.2

Reorder $- 1$ and $- \frac{2 x}{5}$ .

$y = - \frac{2 x}{5} - 1$

Step 1.3

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

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Step 1.3.1

Reorder terms.

$y = - (\frac{2}{5} x) - 1$

Step 1.3.2

Remove parentheses.

$y = - \frac{2}{5} x - 1$

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

$m = - \frac{2}{5}$

$b = - 1$

Step 2.2

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

Slope: $- \frac{2}{5}$

y-intercept: $(0, - 1)$

Slope: $- \frac{2}{5}$

y-intercept: $(0, - 1)$

Step 3

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 3.1

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

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Step 3.1.1

Split the fraction $\frac{5 + 2 x}{5}$ into two fractions.

$y = - (\frac{5}{5} + \frac{2 x}{5})$

Step 3.1.2

Divide $5$ by $5$ .

$y = - (1 + \frac{2 x}{5})$

Step 3.1.3

Write $1$ as a fraction with a common denominator.

$y = - (\frac{5}{5} + \frac{2 x}{5})$

Step 3.1.4

Combine the numerators over the common denominator.

$y = - \frac{5 + 2 x}{5}$

Step 3.1.5

Reorder terms.

$y = - (\frac{1}{5} (5 + 2 x))$

Step 3.1.6

Remove parentheses.

$y = - \frac{1}{5} (5 + 2 x)$

Step 3.2

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

$\begin{array}{c} x & y \\ 0 & - 1 \\ 1 & - \frac{7}{5} \end{array}$

Step 4

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

Slope: $- \frac{2}{5}$

y-intercept: $(0, - 1)$

$\begin{array}{c} x & y \\ 0 & - 1 \\ 1 & - \frac{7}{5} \end{array}$

Step 5