Linear Algebra Examples

$y - 4 = \frac{8}{3} \cdot (x - 3)$

Step 1

Simplify $\frac{8}{3} \cdot (x - 3)$ .

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Step 1.1

Rewrite.

$y - 4 = 0 + 0 + \frac{8}{3} \cdot (x - 3)$

Step 1.2

Simplify by adding zeros.

$y - 4 = \frac{8}{3} \cdot (x - 3)$

Step 1.3

Apply the distributive property.

$y - 4 = \frac{8}{3} x + \frac{8}{3} \cdot - 3$

Step 1.4

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

$y - 4 = \frac{8 x}{3} + \frac{8}{3} \cdot - 3$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Factor $3$ out of $- 3$ .

$y - 4 = \frac{8 x}{3} + \frac{8}{3} \cdot (3 (- 1))$

Step 1.5.2

Cancel the common factor.

$y - 4 = \frac{8 x}{3} + \frac{8}{3} \cdot (3 \cdot - 1)$

Step 1.5.3

Rewrite the expression.

$y - 4 = \frac{8 x}{3} + 8 \cdot - 1$

Step 1.6

Multiply $8$ by $- 1$ .

$y - 4 = \frac{8 x}{3} - 8$

Step 2

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

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Step 2.1

Add $4$ to both sides of the equation.

$y = \frac{8 x}{3} - 8 + 4$

Step 2.2

Add $- 8$ and $4$ .

$y = \frac{8 x}{3} - 4$

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