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\( y = -x - 7 \)
Solución
To solve the equation \( y + 5 = -(x + 2) \) for \( y \), follow these steps:
1. **Distribute the Negative Sign:**
Start by distributing the negative sign on the right-hand side of the equation:
\[
y + 5 = -x - 2
\]
2. **Isolate \( y \):**
To isolate \( y \), subtract 5 from both sides of the equation:
\[
y + 5 - 5 = -x - 2 - 5
\]
Simplifying both sides gives:
\[
y = -x - 7
\]
3. **Final Result:**
The equation solved for \( y \) is:
\[
y = -x - 7
\]
**Interpretation:**
- **Slope-Intercept Form:** The equation \( y = -x - 7 \) is in the slope-intercept form \( y = mx + b \), where:
- \( m = -1 \) is the slope of the line.
- \( b = -7 \) is the y-intercept (the point where the line crosses the y-axis).
- **Graphing the Line:** To graph this equation:
1. Plot the y-intercept at \( (0, -7) \).
2. Use the slope \( -1 \) to determine another point. For example, from \( (0, -7) \), move down 1 unit and to the right 1 unit to reach \( (1, -8) \).
3. Draw a straight line through these points.
**Summary:**
The solution to the equation \( y + 5 = -(x + 2) \) is \( y = -x - 7 \). This represents a straight line with a slope of -1 and a y-intercept at (0, -7).
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Simplifique esta solución Beyond the Answer
To find the solution to the equation \( y + 5 = - (x + 2) \), you can rearrange it to express \( y \) in terms of \( x \): \( y = -x - 2 - 5 \). Simplifying gives you \( y = -x - 7 \). This represents a linear function with a slope of -1 and a y-intercept of -7. Now, think about how this relates to graphing: every time you increase \( x \) by 1, \( y \) decreases by 1. So you could easily plot this by starting at (0, -7) and then using the slope to find other points, creating a nice straight line!
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