To find the correct slope-intercept form of the equation [tex]\(3x - 11y = -22\)[/tex], we need to rearrange the equation into the form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope and [tex]\(b\)[/tex] is the y-intercept. Here are the detailed steps:
1. Start with the given equation:
[tex]\[
3x - 11y = -22
\][/tex]
2. Isolate [tex]\(y\)[/tex] on one side of the equation. To do this, first move the term involving [tex]\(x\)[/tex] to the other side of the equation:
[tex]\[
-11y = -3x - 22
\][/tex]
3. Divide every term by [tex]\(-11\)[/tex] to solve for [tex]\(y\)[/tex]:
[tex]\[
y = \frac{-3x - 22}{-11}
\][/tex]
4. Simplify the equation:
[tex]\[
y = \frac{-3x}{-11} + \frac{-22}{-11}
\][/tex]
Simplifying further:
[tex]\[
y = \frac{3}{11}x + 2
\][/tex]
Thus, the slope-intercept form of the equation [tex]\(3x - 11y = -22\)[/tex] is:
[tex]\[
y = \frac{3}{11}x + 2
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{y = \frac{3}{11} x + 2}
\][/tex]
