Question

14. Which graph matches the linear equation: 6x+y=−4
(1 point)
Responses

Answer 1

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:

1. 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:
1. Passes through the point \((0, -4)\),
2. 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!