Determine if Linear (-9+y)^2-y^2=-11x+8

${(- 9 + y)}^{2} - y^{2} = - 11 x + 8$

Step 1

Solve the equation for $y$ .

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Add $11 x$ to both sides of the equation.

${(- 9 + y)}^{2} - y^{2} + 11 x = 8$

Subtract $8$ from both sides of the equation.

${(- 9 + y)}^{2} - y^{2} + 11 x - 8 = 0$

Simplify ${(- 9 + y)}^{2} - y^{2} + 11 x - 8$ .

Simplify each term.

Rewrite ${(- 9 + y)}^{2}$ as $(- 9 + y) (- 9 + y)$ .

$(- 9 + y) (- 9 + y) - y^{2} + 11 x - 8 = 0$

Expand $(- 9 + y) (- 9 + y)$ using the FOIL Method.

Apply the distributive property.

$- 9 (- 9 + y) + y (- 9 + y) - y^{2} + 11 x - 8 = 0$

Apply the distributive property.

$- 9 \cdot - 9 - 9 y + y (- 9 + y) - y^{2} + 11 x - 8 = 0$

Apply the distributive property.

$- 9 \cdot - 9 - 9 y + y \cdot - 9 + y \cdot y - y^{2} + 11 x - 8 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $- 9$ by $- 9$ .

$81 - 9 y + y \cdot - 9 + y \cdot y - y^{2} + 11 x - 8 = 0$

Move $- 9$ to the left of $y$ .

$81 - 9 y - 9 \cdot y + y \cdot y - y^{2} + 11 x - 8 = 0$

Multiply $y$ by $y$ .

$81 - 9 y - 9 y + y^{2} - y^{2} + 11 x - 8 = 0$

Subtract $9 y$ from $- 9 y$ .

$81 - 18 y + y^{2} - y^{2} + 11 x - 8 = 0$

Combine the opposite terms in $81 - 18 y + y^{2} - y^{2} + 11 x - 8$ .

Subtract $y^{2}$ from $y^{2}$ .

$81 - 18 y + 0 + 11 x - 8 = 0$

Add $81 - 18 y$ and $0$ .

$81 - 18 y + 11 x - 8 = 0$

Subtract $8$ from $81$ .

$- 18 y + 11 x + 73 = 0$

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

Subtract $11 x$ from both sides of the equation.

$- 18 y + 73 = - 11 x$

Subtract $73$ from both sides of the equation.

$- 18 y = - 11 x - 73$

Divide each term in $- 18 y = - 11 x - 73$ by $- 18$ and simplify.

Divide each term in $- 18 y = - 11 x - 73$ by $- 18$ .

$\frac{- 18 y}{- 18} = \frac{- 11 x}{- 18} + \frac{- 73}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 y}{- 18} = \frac{- 11 x}{- 18} + \frac{- 73}{- 18}$

Divide $y$ by $1$ .

$y = \frac{- 11 x}{- 18} + \frac{- 73}{- 18}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{(11) x}{18} + \frac{- 73}{- 18}$

Dividing two negative values results in a positive value.

$y = \frac{11 x}{18} + \frac{73}{18}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear

Determine if Linear (-9+y)^2-y^2=-11x+8

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