Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( y = -2x - 6 \)
Solution
It looks like you're working with the linear equation:
\[
-8x - 4y = 24
\]
If you'd like to solve for \( y \) in terms of \( x \), here's how you can do it step by step:
1. **Start with the original equation:**
\[
-8x - 4y = 24
\]
2. **Isolate the term containing \( y \):**
\[
-4y = 8x + 24
\]
*(By adding \( 8x \) to both sides)*
3. **Solve for \( y \) by dividing both sides by \( -4 \):**
\[
y = \frac{8x + 24}{-4}
\]
\[
y = -2x - 6
\]
So, the equation solved for \( y \) is:
\[
y = -2x - 6
\]
**Graphical Interpretation:**
This equation is in the slope-intercept form \( y = mx + b \), where:
- **Slope (\( m \))**: -2
- **Y-intercept (\( b \))**: -6
This means the line crosses the \( y \)-axis at (0, -6) and has a slope of -2, indicating it decreases by 2 units vertically for every 1 unit it moves horizontally to the right.
**Example: Plotting the Line**
To graph the equation \( y = -2x - 6 \):
1. **Plot the Y-intercept:**
- Start at (0, -6) on the graph.
2. **Use the slope to find another point:**
- From (0, -6), move down 2 units and to the right 1 unit to reach (1, -8).
3. **Draw the line:**
- Connect the two points with a straight line extending in both directions.
This visual representation can help in understanding the relationship between \( x \) and \( y \) as defined by the equation.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To solve \( -8x - 4y = 24 \), you can start by simplifying it. Divide the entire equation by -4, giving you \( 2x + y = -6 \). Now, you can express \( y \) in terms of \( x \): \( y = -2x - 6 \). This is the equation of a straight line, which can be graphed easily to see all the solutions! If you want to find specific points, you can choose values for \( x \). For example, if \( x = 0 \), then \( y = -6 \), while if \( x = 1 \), \( y = -8 \). Don’t forget that plotting two points is all you need to sketch the line accurately!
