Linear Algebra Examples

$4 (x - 8) = 5 (y - 9)$

Step 1

Rewrite the equation as $5 (y - 9) = 4 (x - 8)$ .

$5 (y - 9) = 4 (x - 8)$

Step 2

Divide each term in $5 (y - 9) = 4 (x - 8)$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 (y - 9) = 4 (x - 8)$ by $5$ .

$\frac{5 (y - 9)}{5} = \frac{4 (x - 8)}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 (y - 9)}{5} = \frac{4 (x - 8)}{5}$

Step 2.2.1.2

Divide $y - 9$ by $1$ .

$y - 9 = \frac{4 (x - 8)}{5}$

Step 3

Add $9$ to both sides of the equation.

$y = \frac{4 (x - 8)}{5} + 9$

Step 4

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 5