To find the graph that matches the linear equation \(6x + y = -4\), we can rewrite this equation in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
Starting with the equation:
- Rearrange it to isolate \(y\): \[ y = -6x - 4 \]
Now, we can see that:
- The slope (\(m\)) is \(-6\).
- The y-intercept (\(b\)) is \(-4\). This means the line crosses the y-axis at the point \((0, -4)\).
To find points on the graph, you can also calculate a point by substituting values for \(x\):
For \(x = 0\): \[ y = -6(0) - 4 = -4 \quad \text{(Point: (0, -4))} \]
For \(x = 1\): \[ y = -6(1) - 4 = -10 \quad \text{(Point: (1, -10))} \]
For \(x = -1\): \[ y = -6(-1) - 4 = 2 \quad \text{(Point: (-1, 2))} \]
Now, using these points:
- The line passes through \((0, -4)\), \((1, -10)\), and \((-1, 2)\).
- The line will slope downward from left to right (due to the negative slope).
When looking at the provided graph options, you should select the one that:
- Passes through the point \((0, -4)\),
- Has a negative slope.
If you have graphs available, choose the one that satisfies these conditions. If you describe or upload them, I would be happy to help identify the correct one!
1 answer