We start with the given equation:

$2x + 5y = -5$

Step 1: Convert to Slope-Intercept Form ($y = mx + b$)

The slope-intercept form is:

$y = mx + b$

where:

• $m$ is the slope
• $b$ is the y-intercept

Solve for $y$:

$5y = -2x - 5$

$y = -\frac{2}{5}x - 1$

Step 2: Identify the Slope and Y-Intercept

From the equation:

$y = -\frac{2}{5}x - 1$

• Slope ($m$) = $-\frac{2}{5}$
• Y-Intercept ($b$) = $-1$ (which corresponds to the point $(0, -1)$)

Step 3: Graphing the Line

1. Plot the Y-Intercept: Start by plotting the point $(0, -1)$.
2. Use the Slope: The slope $-\frac{2}{5}$ means:
   • Move down 2 units (negative direction).
   • Move right 5 units (positive direction).
   • Plot this second point.
3. Draw the Line: Connect the points with a straight line extending in both directions.

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Would you like a visual graph? Let me know!

Related Questions:

1. How do you find the x-intercept of this equation?
2. What happens to the graph if the equation changes to $2x + 5y = 5$?
3. How can you verify the slope using two points on the line?
4. What does a positive slope indicate compared to a negative slope?
5. How do you determine if two lines are parallel?

Tip:

To check if a point is on the line, substitute its $x$ and $y$ values into the equation. If both sides are equal, the point lies on the line.