To determine if the equation [tex]\(-8y = 9 - x\)[/tex] is a linear equation, we need to follow a few steps to understand its structure.
1. Start with the given equation:
[tex]\[
-8y = 9 - x
\][/tex]
2. Rearrange the equation to observe its form:
First, we want to isolate [tex]\( y \)[/tex]. To do that, we'll express [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex].
[tex]\[
-8y = -x + 9
\][/tex]
3. Divide every term by [tex]\(-8\)[/tex] to solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{1}{8} x - \frac{9}{8}
\][/tex]
4. Analyze the resulting equation:
After rearranging, we see that the equation is now written as:
[tex]\[
y = \frac{1}{8} x - \frac{9}{8}
\][/tex]
This equation is in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] (the coefficient of [tex]\(x\)[/tex]) and [tex]\( b \)[/tex] (the constant term) are constants.
5. Conclude about the type of equation:
The equation [tex]\( y = \frac{1}{8} x - \frac{9}{8} \)[/tex] is a linear equation because it can be written in the form [tex]\( y = mx + b \)[/tex], which is the slope-intercept form of a linear equation.
Therefore, the equation [tex]\(-8y = 9 - x\)[/tex] is a linear equation, and we can confidently say yes.
