Finite Math Examples

$y = \frac{1}{2} x + 5$ , $2 y = x + 10$

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 the right side.

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Step 1.2.1

Combine $\frac{1}{2}$ and $x$ .

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

Step 1.3

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is $\frac{1}{2}$ .

$m_{1} = \frac{1}{2}$

Step 3

Rewrite in slope-intercept form.

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Step 3.1

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 3.2

Divide each term in $2 y = x + 10$ by $2$ and simplify.

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Step 3.2.1

Divide each term in $2 y = x + 10$ by $2$ .

$\frac{2 y}{2} = \frac{x}{2} + \frac{10}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{x}{2} + \frac{10}{2}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{x}{2} + \frac{10}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $10$ by $2$ .

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

Step 3.3

Reorder terms.

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

Step 4

Using the slope-intercept form, the slope is $\frac{1}{2}$ .

$m_{2} = \frac{1}{2}$

Step 5

Since the slopes are the same, the lines are on top of one another, so the system has an infinite number of solutions.

$m_{1} = \frac{1}{2}$

$m_{2} = \frac{1}{2}$

Step 6