Pre-Algebra Examples

$10 x = - 5 y$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $- 5 y = 10 x$ .

$- 5 y = 10 x$

Step 1.2

Divide each term in $- 5 y = 10 x$ by $- 5$ and simplify.

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Step 1.2.1

Divide each term in $- 5 y = 10 x$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{10 x}{- 5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{10 x}{- 5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{10 x}{- 5}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Cancel the common factor of $10$ and $- 5$ .

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Step 1.2.3.1.1

Factor $5$ out of $10 x$ .

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

Step 1.2.3.1.2

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

$y = - 1 \cdot (2 x)$

Step 1.2.3.2

Simplify the expression.

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Step 1.2.3.2.1

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

$y = - (2 x)$

Step 1.2.3.2.2

Multiply $2$ by $- 1$ .

$y = - 2 x$

Step 2

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

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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

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

$m = - 2$

$b = 0$

Step 2.3

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

Slope: $- 2$

y-intercept: $(0, 0)$

Slope: $- 2$

y-intercept: $(0, 0)$

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

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

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & - 2 \end{array}$

Step 4

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

Slope: $- 2$

y-intercept: $(0, 0)$

$\begin{array}{c} x & y \\ 0 & 0 \\ 1 & - 2 \end{array}$

Step 5