Question

determine if the following equation is linear. if the equation is linear, convert it to standard form: ( ax + by = c ). ((-7 + y)^2 - y^2 = -x + 7)
answer
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( square ) linear standard form:
( \bigcirc ) not linear

Explanation:

Step1: Expand the squared term

$$(-7+y)^2 = y^2 -14y + 49$$

Step2: Substitute into original equation

$$y^2 -14y + 49 - y^2 = -x + 7$$

Step3: Simplify left-hand side

$$-14y + 49 = -x + 7$$

Step4: Rearrange to standard form

$$x -14y = 7 - 49$$
$$x -14y = -42$$

Answer:

Linear
Standard Form: $x - 14y = -42$