Finite Math Examples

$\frac{1}{2} y = - 4 x + 12$

Step 1

Solve for $y$ .

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Step 1.1

Multiply both sides of the equation by $2$ .

$2 \frac{y}{2} = 2 (- 4 x + 12)$

Step 1.2

Simplify both sides of the equation.

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Step 1.2.1

Simplify the left side.

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Step 1.2.1.1

Cancel the common factor of $2$ .

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Step 1.2.1.1.1

Cancel the common factor.

$2 \frac{y}{2} = 2 (- 4 x + 12)$

Step 1.2.1.1.2

Rewrite the expression.

$y = 2 (- 4 x + 12)$

Step 1.2.2

Simplify the right side.

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Step 1.2.2.1

Simplify $2 (- 4 x + 12)$ .

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Step 1.2.2.1.1

Apply the distributive property.

$y = 2 (- 4 x) + 2 \cdot 12$

Step 1.2.2.1.2

Multiply.

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Step 1.2.2.1.2.1

Multiply $- 4$ by $2$ .

$y = - 8 x + 2 \cdot 12$

Step 1.2.2.1.2.2

Multiply $2$ by $12$ .

$y = - 8 x + 24$

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 $y = m x + b$ .

$m = - 8$

$b = 24$

Step 2.3

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

Slope: $- 8$

y-intercept: $(0, 24)$

Slope: $- 8$

y-intercept: $(0, 24)$

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.

$\begin{array}{c} x & y \\ 0 & 24 \\ 1 & 16 \end{array}$

Step 4

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

Slope: $- 8$

y-intercept: $(0, 24)$

$\begin{array}{c} x & y \\ 0 & 24 \\ 1 & 16 \end{array}$

Step 5