Question

Which graph matches the linear equation: 6x + y = -4
A. (0, -4), (1, -10)
B. (3, 0), (0, -2)
C. (0, 2), (1, -1)
D. (1, 2), (0, -4)

Answer 1

To determine which graph represents the linear equation \(6x + y = -4\), we can convert the equation into slope-intercept form and then check the given points.

First, let's rearrange the equation:

\[
y = -6x - 4
\]

Now, we can check each option by substituting the \(x\) value into the equation to see if we get the corresponding \(y\) value.

**Option A: (0, -4), (1, -10)**
1. For \(x = 0\):
\[
y = -6(0) - 4 = -4 \quad \text{(matches)}
\]
2. For \(x = 1\):
\[
y = -6(1) - 4 = -6 - 4 = -10 \quad \text{(matches)}
\]

This option works.

**Option B: (3, 0), (0, -2)**
1. For \(x = 3\):
\[
y = -6(3) - 4 = -18 - 4 = -22 \quad \text{(does not match)}
\]

This option does not work.

**Option C: (0, 2), (1, -1)**
1. For \(x = 0\):
\[
y = -6(0) - 4 = -4 \quad \text{(does not match)}
\]

This option does not work.

**Option D: (1, 2), (0, -4)**
1. For \(x = 1\):
\[
y = -6(1) - 4 = -6 - 4 = -10 \quad \text{(does not match)}
\]

This option does not work.

Therefore, the correct matching graph for the linear equation \(6x + y = -4\) is **Option A: (0, -4), (1, -10)**.