Find Three Ordered Pair Solutions y=-5/6x+2

$y = - \frac{5}{6} x + 2$

Step 1

Simplify each term.

Combine $x$ and $\frac{5}{6}$ .

$y = - \frac{x \cdot 5}{6} + 2$

Move $5$ to the left of $x$ .

$y = - \frac{5 x}{6} + 2$

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.

Remove parentheses.

$y = - \frac{5 (0)}{6} + 2$

Simplify $- \frac{5 (0)}{6} + 2$ .

Simplify each term.

Cancel the common factor of $0$ and $6$ .

Factor $6$ out of $5 (0)$ .

$y = - \frac{6 (5 \cdot (0))}{6} + 2$

Cancel the common factors.

Factor $6$ out of $6$ .

$y = - \frac{6 (5 \cdot (0))}{6 (1)} + 2$

Cancel the common factor.

$y = - \frac{6 (5 \cdot (0))}{6 \cdot 1} + 2$

Rewrite the expression.

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

Divide $5 \cdot (0)$ by $1$ .

$y = - (5 \cdot (0)) + 2$

Multiply $- (5 \cdot (0))$ .

Multiply $5$ by $0$ .

$y = - 0 + 2$

Multiply $- 1$ by $0$ .

$y = 0 + 2$

Add $0$ and $2$ .

$y = 2$

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

$(0, 2)$

Step 4

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

Remove parentheses.

$y = - \frac{5 (1)}{6} + 2$

Simplify $- \frac{5 (1)}{6} + 2$ .

Multiply $5$ by $1$ .

$y = - \frac{5}{6} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = - \frac{5}{6} + 2 \cdot \frac{6}{6}$

Combine $2$ and $\frac{6}{6}$ .

$y = - \frac{5}{6} + \frac{2 \cdot 6}{6}$

Combine the numerators over the common denominator.

$y = \frac{- 5 + 2 \cdot 6}{6}$

Simplify the numerator.

Multiply $2$ by $6$ .

$y = \frac{- 5 + 12}{6}$

Add $- 5$ and $12$ .

$y = \frac{7}{6}$

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

$(1, \frac{7}{6})$

Step 5

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

Remove parentheses.

$y = - \frac{5 (2)}{6} + 2$

Simplify $- \frac{5 (2)}{6} + 2$ .

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $5 (2)$ .

$y = - \frac{2 \cdot 5}{6} + 2$

Cancel the common factors.

Factor $2$ out of $6$ .

$y = - \frac{2 \cdot 5}{2 \cdot 3} + 2$

Cancel the common factor.

$y = - \frac{2 \cdot 5}{2 \cdot 3} + 2$

Rewrite the expression.

$y = - \frac{5}{3} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{5}{3} + 2 \cdot \frac{3}{3}$

Combine $2$ and $\frac{3}{3}$ .

$y = - \frac{5}{3} + \frac{2 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 5 + 2 \cdot 3}{3}$

Simplify the numerator.

Multiply $2$ by $3$ .

$y = \frac{- 5 + 6}{3}$

Add $- 5$ and $6$ .

$y = \frac{1}{3}$

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

$(2, \frac{1}{3})$

Step 6

These are three possible solutions to the equation.

$(0, 2), (1, \frac{7}{6}), (2, \frac{1}{3})$

Step 7

Find Three Ordered Pair Solutions y=-5/6x+2

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