Pre-Algebra Examples

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

Step 1

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

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Step 1.1

Add $5$ to both sides of the equation.

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

Step 1.2

To write $5$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.3

Combine $5$ and $\frac{5}{5}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $5$ by $5$ .

$y = \frac{x}{5} + \frac{- 2 + 25}{5}$

Step 1.5.2

Add $- 2$ and $25$ .

$y = \frac{x}{5} + \frac{23}{5}$

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

Reorder terms.

$y = \frac{1}{5} x + \frac{23}{5}$

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 $y = m x + b$ .

$m = \frac{1}{5}$

$b = \frac{23}{5}$

Step 3.2

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

Slope: $\frac{1}{5}$

y-intercept: $(0, \frac{23}{5})$

Slope: $\frac{1}{5}$

y-intercept: $(0, \frac{23}{5})$

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

Reorder terms.

$y = \frac{1}{5} x + \frac{23}{5}$

Step 4.2

Find the x-intercept.

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Step 4.2.1

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

$0 = \frac{1}{5} x + \frac{23}{5}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $\frac{1}{5} x + \frac{23}{5} = 0$ .

$\frac{1}{5} x + \frac{23}{5} = 0$

Step 4.2.2.2

Combine $\frac{1}{5}$ and $x$ .

$\frac{x}{5} + \frac{23}{5} = 0$

Step 4.2.2.3

Subtract $\frac{23}{5}$ from both sides of the equation.

$\frac{x}{5} = - \frac{23}{5}$

Step 4.2.2.4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = - 23$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(- 23, 0)$

Step 4.3

Find the y-intercept.

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Step 4.3.1

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

$y = \frac{1}{5} \cdot (0) + \frac{23}{5}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Multiply $\frac{1}{5}$ by $0$ .

$y = \frac{1}{5} \cdot 0 + \frac{23}{5}$

Step 4.3.2.2

Remove parentheses.

$y = \frac{1}{5} \cdot (0) + \frac{23}{5}$

Step 4.3.2.3

Simplify $\frac{1}{5} \cdot (0) + \frac{23}{5}$ .

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Step 4.3.2.3.1

Multiply $\frac{1}{5}$ by $0$ .

$y = 0 + \frac{23}{5}$

Step 4.3.2.3.2

Add $0$ and $\frac{23}{5}$ .

$y = \frac{23}{5}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{23}{5})$

Step 4.4

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

$\begin{array}{c} x & y \\ - 23 & 0 \\ 0 & \frac{23}{5} \end{array}$

Step 5

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

Slope: $\frac{1}{5}$

y-intercept: $(0, \frac{23}{5})$

$\begin{array}{c} x & y \\ - 23 & 0 \\ 0 & \frac{23}{5} \end{array}$

Step 6