Pre-Algebra Examples

$10 x - 5 y + 8 = 0$

Step 1

Solve for $y$ .

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Step 1.1

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

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Step 1.1.1

Subtract $10 x$ from both sides of the equation.

$- 5 y + 8 = - 10 x$

Step 1.1.2

Subtract $8$ from both sides of the equation.

$- 5 y = - 10 x - 8$

Step 1.2

Divide each term in $- 5 y = - 10 x - 8$ by $- 5$ and simplify.

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Step 1.2.1

Divide each term in $- 5 y = - 10 x - 8$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 10 x}{- 5} + \frac{- 8}{- 5}$

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.

$\frac{- 5 y}{- 5} = \frac{- 10 x}{- 5} + \frac{- 8}{- 5}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 10 x}{- 5} + \frac{- 8}{- 5}$

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

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

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Step 1.2.3.1.1.1

Factor $- 5$ out of $- 10 x$ .

$y = \frac{- 5 (2 x)}{- 5} + \frac{- 8}{- 5}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $- 5$ out of $- 5$ .

$y = \frac{- 5 (2 x)}{- 5 (1)} + \frac{- 8}{- 5}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{- 5 (2 x)}{- 5 \cdot 1} + \frac{- 8}{- 5}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{2 x}{1} + \frac{- 8}{- 5}$

Step 1.2.3.1.1.2.4

Divide $2 x$ by $1$ .

$y = 2 x + \frac{- 8}{- 5}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

$y = 2 x + \frac{8}{5}$

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 $y = m x + b$ .

$m = 2$

$b = \frac{8}{5}$

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: $(0, \frac{8}{5})$

Slope: $2$

y-intercept: $(0, \frac{8}{5})$

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

Find the x-intercept.

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Step 3.1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = 2 x + \frac{8}{5}$

Step 3.1.2

Solve the equation.

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Step 3.1.2.1

Rewrite the equation as $2 x + \frac{8}{5} = 0$ .

$2 x + \frac{8}{5} = 0$

Step 3.1.2.2

Subtract $\frac{8}{5}$ from both sides of the equation.

$2 x = - \frac{8}{5}$

Step 3.1.2.3

Divide each term in $2 x = - \frac{8}{5}$ by $2$ and simplify.

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Step 3.1.2.3.1

Divide each term in $2 x = - \frac{8}{5}$ by $2$ .

$\frac{2 x}{2} = \frac{- \frac{8}{5}}{2}$

Step 3.1.2.3.2

Simplify the left side.

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Step 3.1.2.3.2.1

Cancel the common factor of $2$ .

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Step 3.1.2.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- \frac{8}{5}}{2}$

Step 3.1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \frac{8}{5}}{2}$

Step 3.1.2.3.3

Simplify the right side.

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Step 3.1.2.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{8}{5} \cdot \frac{1}{2}$

Step 3.1.2.3.3.2

Cancel the common factor of $2$ .

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Step 3.1.2.3.3.2.1

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$x = \frac{- 8}{5} \cdot \frac{1}{2}$

Step 3.1.2.3.3.2.2

Factor $2$ out of $- 8$ .

$x = \frac{2 (- 4)}{5} \cdot \frac{1}{2}$

Step 3.1.2.3.3.2.3

Cancel the common factor.

$x = \frac{2 \cdot - 4}{5} \cdot \frac{1}{2}$

Step 3.1.2.3.3.2.4

Rewrite the expression.

$x = \frac{- 4}{5}$

Step 3.1.2.3.3.3

Move the negative in front of the fraction.

$x = - \frac{4}{5}$

Step 3.1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{4}{5}, 0)$

Step 3.2

Find the y-intercept.

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Step 3.2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = 2 (0) + \frac{8}{5}$

Step 3.2.2

Solve the equation.

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Step 3.2.2.1

Remove parentheses.

$y = 2 (0) + \frac{8}{5}$

Step 3.2.2.2

Simplify $2 (0) + \frac{8}{5}$ .

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Step 3.2.2.2.1

Multiply $2$ by $0$ .

$y = 0 + \frac{8}{5}$

Step 3.2.2.2.2

Add $0$ and $\frac{8}{5}$ .

$y = \frac{8}{5}$

Step 3.2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{8}{5})$

Step 3.3

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

$\begin{array}{c} x & y \\ - \frac{4}{5} & 0 \\ 0 & \frac{8}{5} \end{array}$

Step 4

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

Slope: $2$

y-intercept: $(0, \frac{8}{5})$

$\begin{array}{c} x & y \\ - \frac{4}{5} & 0 \\ 0 & \frac{8}{5} \end{array}$

Step 5