Linear Algebra Examples

$y - 4 = \frac{3}{5} \cdot (x - 3)$

Step 1

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

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Step 1.1

Rewrite.

$y - 4 = 0 + 0 + \frac{3}{5} \cdot (x - 3)$

Step 1.2

Simplify by adding zeros.

$y - 4 = \frac{3}{5} \cdot (x - 3)$

Step 1.3

Apply the distributive property.

$y - 4 = \frac{3}{5} x + \frac{3}{5} \cdot - 3$

Step 1.4

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

$y - 4 = \frac{3 x}{5} + \frac{3}{5} \cdot - 3$

Step 1.5

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

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Step 1.5.1

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

$y - 4 = \frac{3 x}{5} + \frac{3 \cdot - 3}{5}$

Step 1.5.2

Multiply $3$ by $- 3$ .

$y - 4 = \frac{3 x}{5} + \frac{- 9}{5}$

Step 1.6

Move the negative in front of the fraction.

$y - 4 = \frac{3 x}{5} - \frac{9}{5}$

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.

$y = \frac{3 x}{5} - \frac{9}{5} + 4$

Step 2.2

To write $4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{3 x}{5} - \frac{9}{5} + 4 \cdot \frac{5}{5}$

Step 2.3

Combine $4$ and $\frac{5}{5}$ .

$y = \frac{3 x}{5} - \frac{9}{5} + \frac{4 \cdot 5}{5}$

Step 2.4

Combine the numerators over the common denominator.

$y = \frac{3 x}{5} + \frac{- 9 + 4 \cdot 5}{5}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $4$ by $5$ .

$y = \frac{3 x}{5} + \frac{- 9 + 20}{5}$

Step 2.5.2

Add $- 9$ and $20$ .

$y = \frac{3 x}{5} + \frac{11}{5}$

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