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)
- For \(x = 0\): \[ y = -6(0) - 4 = -4 \quad \text{(matches)} \]
- For \(x = 1\): \[ y = -6(1) - 4 = -6 - 4 = -10 \quad \text{(matches)} \]
This option works.
Option B: (3, 0), (0, -2)
- 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)
- For \(x = 0\): \[ y = -6(0) - 4 = -4 \quad \text{(does not match)} \]
This option does not work.
Option D: (1, 2), (0, -4)
- 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).
1 answer