Question

Determine if the following equation is linear. if the equation is linear, convert it to standard form: ax by=c a x b y = c . x2−(x−5)2=9y

Answer 1

The given equation x^2 - (x-5)^2 = 9y is not linear. To convert it to standard form, we rearrange the terms to get 10x - 9y = -25.

Step-by-step explanation:

The equation x^2 - (x-5)^2 = 9y is not linear. In a linear equation, the highest power of the variable is 1. The given equation includes the term (x-5)^2, which is quadratic because it has a power of 2.

To convert the equation to standard form, we need to rearrange it so that all the terms are on one side and the constant is on the other side. First, let's expand (x-5)^2:

x^2 - (x-5)^2 = 9y

x^2 - (x^2 - 10x + 25) = 9y

Simplifying, we get:

-10x + 25 = 9y

Now, let's rearrange the equation by moving the variables to one side and the constant to the other side:

10x - 9y = -25

So, the equation in standard form is 10x - 9y = -25.