Algebra Examples

$y - 1 = \frac{1}{5} (x + 2)$

Step 1

Solve the equation for $y$ .

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Step 1.1

Simplify $\frac{1}{5} \cdot (x + 2)$ .

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Step 1.1.1

Rewrite.

$y - 1 = 0 + 0 + \frac{1}{5} \cdot (x + 2)$

Step 1.1.2

Simplify by adding zeros.

$y - 1 = \frac{1}{5} \cdot (x + 2)$

Step 1.1.3

Apply the distributive property.

$y - 1 = \frac{1}{5} x + \frac{1}{5} \cdot 2$

Step 1.1.4

Combine $\frac{1}{5}$ and $x$ .

$y - 1 = \frac{x}{5} + \frac{1}{5} \cdot 2$

Step 1.1.5

Combine $\frac{1}{5}$ and $2$ .

$y - 1 = \frac{x}{5} + \frac{2}{5}$

Step 1.2

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

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Step 1.2.1

Add $1$ to both sides of the equation.

$y = \frac{x}{5} + \frac{2}{5} + 1$

Step 1.2.2

Write $1$ as a fraction with a common denominator.

$y = \frac{x}{5} + \frac{2}{5} + \frac{5}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

$y = \frac{x}{5} + \frac{2 + 5}{5}$

Step 1.2.4

Add $2$ and $5$ .

$y = \frac{x}{5} + \frac{7}{5}$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

$y = \frac{0}{5} + \frac{7}{5}$

Step 3.2

Simplify $\frac{0}{5} + \frac{7}{5}$ .

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Step 3.2.1

Combine the numerators over the common denominator.

$y = \frac{0 + 7}{5}$

Step 3.2.2

Add $0$ and $7$ .

$y = \frac{7}{5}$

Step 3.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, \frac{7}{5})$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = \frac{1}{5} + \frac{7}{5}$

Step 4.2

Simplify $\frac{1}{5} + \frac{7}{5}$ .

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Step 4.2.1

Combine the numerators over the common denominator.

$y = \frac{1 + 7}{5}$

Step 4.2.2

Add $1$ and $7$ .

$y = \frac{8}{5}$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, \frac{8}{5})$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = \frac{2}{5} + \frac{7}{5}$

Step 5.2

Simplify $\frac{2}{5} + \frac{7}{5}$ .

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Step 5.2.1

Combine the numerators over the common denominator.

$y = \frac{2 + 7}{5}$

Step 5.2.2

Add $2$ and $7$ .

$y = \frac{9}{5}$

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{9}{5})$

Step 6

These are three possible solutions to the equation.

$(0, \frac{7}{5}), (1, \frac{8}{5}), (2, \frac{9}{5})$

Step 7