Question

Rewrite the linear inequality in slope-intercept form (i.e. solve for y).

5x + 3y > -5

Answer 1

To rewrite the inequality \( 5x + 3y > -5 \) in slope-intercept form (which is \( y = mx + b \)), follow these steps:

1. Start with the original inequality:
\[
5x + 3y > -5
\]

2. Subtract \( 5x \) from both sides:
\[
3y > -5 - 5x
\]

3. Rewrite the right side:
\[
3y > -5x - 5
\]

4. Now, divide every term by \( 3 \) to solve for \( y \):
\[
y > -\frac{5}{3}x - \frac{5}{3}
\]

So the linear inequality in slope-intercept form is:
\[
y > -\frac{5}{3}x - \frac{5}{3}
\]