Linear Algebra Examples

$y - 8 = \frac{5}{3} \cdot (x - 5)$

Step 1

Simplify $\frac{5}{3} \cdot (x - 5)$ .

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Step 1.1

Rewrite.

$y - 8 = 0 + 0 + \frac{5}{3} \cdot (x - 5)$

Step 1.2

Simplify by adding zeros.

$y - 8 = \frac{5}{3} \cdot (x - 5)$

Step 1.3

Apply the distributive property.

$y - 8 = \frac{5}{3} x + \frac{5}{3} \cdot - 5$

Step 1.4

Combine $\frac{5}{3}$ and $x$ .

$y - 8 = \frac{5 x}{3} + \frac{5}{3} \cdot - 5$

Step 1.5

Multiply $\frac{5}{3} \cdot - 5$ .

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Step 1.5.1

Combine $\frac{5}{3}$ and $- 5$ .

$y - 8 = \frac{5 x}{3} + \frac{5 \cdot - 5}{3}$

Step 1.5.2

Multiply $5$ by $- 5$ .

$y - 8 = \frac{5 x}{3} + \frac{- 25}{3}$

Step 1.6

Move the negative in front of the fraction.

$y - 8 = \frac{5 x}{3} - \frac{25}{3}$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Add $8$ to both sides of the equation.

$y = \frac{5 x}{3} - \frac{25}{3} + 8$

Step 2.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{5 x}{3} - \frac{25}{3} + 8 \cdot \frac{3}{3}$

Step 2.3

Combine $8$ and $\frac{3}{3}$ .

$y = \frac{5 x}{3} - \frac{25}{3} + \frac{8 \cdot 3}{3}$

Step 2.4

Combine the numerators over the common denominator.

$y = \frac{5 x}{3} + \frac{- 25 + 8 \cdot 3}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $8$ by $3$ .

$y = \frac{5 x}{3} + \frac{- 25 + 24}{3}$

Step 2.5.2

Add $- 25$ and $24$ .

$y = \frac{5 x}{3} + \frac{- 1}{3}$

Step 2.6

Move the negative in front of the fraction.

$y = \frac{5 x}{3} - \frac{1}{3}$

Step 3

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 4