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To find the slope and y-intercept of the line given by the equation:

\[
2x + 5y = -4
\]

we need to rewrite this equation in slope-intercept form, which is:

\[
y = mx + b
\]

where \(m\) represents the slope and \(b\) represents the y-intercept.

### Step-by-step process:

1. Start with the given equation:
   \[
   2x + 5y = -4
   \]

2. Solve for \(y\) by isolating \(y\) on one side of the equation. Subtract \(2x\) from both sides:
   \[
   5y = -2x - 4
   \]

3. Divide every term by 5 to solve for \(y\):
   \[
   y = \frac{-2}{5}x - \frac{4}{5}
   \]

Now that we have the equation in slope-intercept form \(y = mx + b\), we can identify the slope and y-intercept:

- The slope \(m = \frac{-2}{5}\)
- The y-intercept \(b = \frac{-4}{5}\)

Thus:
- Slope: \(\frac{-2}{5}\)
- Y-intercept: \(\frac{-4}{5}\)

Would you like more details on the steps, or do you have any other questions?

Here are some follow-up questions:

1. Can you convert any line equation into slope-intercept form?
2. How do you interpret the slope of a line in a real-world context?
3. What happens when the slope is zero? How does the line look?
4. How would the equation change if the slope were positive?
5. Can you calculate the x-intercept from this equation?

**Tip:** The slope tells you how steep a line is, while the y-intercept is the point where the line crosses the y-axis.

Find the slope and the y-intercept of the line. 2x + 5y = -4

Discover how to find the slope and y-intercept of the equation 2x + 5y = -4. This step-by-step guide breaks down the process of converting a linear equation into slope-intercept form, with detailed explanations for algebra students.

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