To graph the equation $4x + 5y = -20$, follow these steps:

Step 1: Rewrite in Slope-Intercept Form

To make it easier to graph, solve for $y$ in terms of $x$: $4x + 5y = -20$ Subtract $4x$ from both sides: $5y = -4x - 20$ Divide through by $5$: $y = -\frac{4}{5}x - 4$ Now the equation is in the form $y = mx + b$, where:

• Slope ($m$) = $-\frac{4}{5}$
• Y-intercept ($b$) = $-4$

Step 2: Plot the Y-Intercept

Start by plotting the y-intercept, $-4$, on the y-axis.

Step 3: Use the Slope to Find Another Point

The slope $-\frac{4}{5}$ means:

• Move 4 units down (negative rise) and 5 units to the right (positive run).

From the y-intercept $(0, -4)$:

1. Move down 4 units to $-8$ on the y-axis.
2. Move right 5 units to $(5, -8)$.

Plot the point $(5, -8)$.

Step 4: Draw the Line

Draw a straight line through the points $(0, -4)$ and $(5, -8)$. Extend the line in both directions.

Would you like me to graph it for you, or do you want any further clarification?

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Relative Questions:

1. How can the slope-intercept form be used to analyze the steepness of a line?
2. What does the y-intercept represent in a linear equation?
3. Can this equation be rearranged into other forms, such as standard form or point-slope form?
4. How would the graph change if the slope were positive instead of negative?
5. What are the x-intercept and its significance for this equation?

Tip: Always double-check calculations when rearranging equations to avoid small algebraic errors!