Finite Math Examples

$z = 0.4 x + 1.5 y$

Step 1

Move all terms containing variables to the left side of the equation.

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Step 1.1

Subtract

$0.4 x$ from both sides of the equation.

$z - 0.4 x = 1.5 y$

Step 1.2

Subtract

$1.5 y$ from both sides of the equation.

$z - 0.4 x - 1.5 y = 0$

Step 1.3

Move

$z$ .

$- 0.4 x - 1.5 y + z = 0$

Step 2

This is the form of a hyperbola. Use this form to determine the values used to find the asymptotes of the hyperbola.

$\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$

Step 3

Match the values in this hyperbola to those of the standard form. The variable

$h$ represents the x-offset from the origin,

$k$ represents the y-offset from origin,

$a$ .

$a = 1$

$b = 1$

$k = 0$

$h = 0$

Step 4

The asymptotes follow the form

$y = \pm \frac{b (x - h)}{a} + k$ because this hyperbola opens left and right.

$y = \pm 1 \cdot x + 0$

Step 5

Simplify

$1 \cdot x + 0$ .

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Step 5.1

Add

$1 \cdot x$ and

$0$ .

$y = 1 \cdot x$

Step 5.2

Multiply

$x$ by

$1$ .

$y = x$

Step 6

Simplify

$- 1 \cdot x + 0$ .

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Step 6.1

Add

$- 1 \cdot x$ and

$0$ .

$y = - 1 \cdot x$

Step 6.2

Rewrite

$- 1 x$ as

$- x$ .

$y = - x$

Step 7

This hyperbola has two asymptotes.

$y = x, y = - x$

Step 8

The asymptotes are

$y = x$ and

$y = - x$ .

Asymptotes:

$y = x, y = - x$

Step 9