Finite Math Examples

$z = 5 x - y$

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

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

$5 x - y = z$

Step 1.3

Subtract $5 x$ from both sides of the equation.

$- y = z - 5 x$

Step 1.4

Divide each term in $- y = z - 5 x$ by $- 1$ and simplify.

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Step 1.4.1

Divide each term in $- y = z - 5 x$ by $- 1$ .

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

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Dividing two negative values results in a positive value.

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

Step 1.4.2.2

Divide $y$ by $1$ .

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

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

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

$y = - 1 \cdot z + \frac{- 5 x}{- 1}$

Step 1.4.3.1.2

Rewrite $- 1 \cdot z$ as $- z$ .

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

Step 1.4.3.1.3

Move the negative one from the denominator of $\frac{- 5 x}{- 1}$ .

$y = - z - 1 \cdot (- 5 x)$

Step 1.4.3.1.4

Rewrite $- 1 \cdot (- 5 x)$ as $- (- 5 x)$ .

$y = - z - (- 5 x)$

Step 1.4.3.1.5

Multiply $- 5$ by $- 1$ .

$y = - z + 5 x$

Step 2

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

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Step 2.1

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

$m = - 1$

$b = 5 x$

Step 2.2

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

Slope: $- 1$

y-intercept: $(0, 5 x)$

Slope: $- 1$

y-intercept: $(0, 5 x)$

Step 3