To determine which graph represents the equation \( x - 4y = -4 \), we can rearrange this equation into slope-intercept form \( y = mx + b \).
Starting with the given equation:
\[ x - 4y = -4 \]
We can isolate \( y \) as follows:
- Subtract \( x \) from both sides:
\[ -4y = -x - 4 \]
- Divide each term by \(-4\):
\[ y = \frac{1}{4}x + 1 \]
Now we can identify the slope and y-intercept from this:
- The slope (\( m \)) is \( \frac{1}{4} \),
- The y-intercept (\( b \)) is \( 1 \).
Using the slope and the y-intercept, we can find a couple of points on the graph of the line.
- The y-intercept indicates that when \( x = 0 \), \( y = 1 \). So, one point is \( (0, 1) \).
- To find another point, let’s use the x-intercept. Set \( y = 0 \):
\[ 0 = \frac{1}{4}x + 1 \ \frac{1}{4}x = -1 \ x = -4 \]
So, another point is \( (-4, 0) \).
Now we have two points: \( (0, 1) \) and \( (-4, 0) \).
Now, let's evaluate the options:
- A coordinate plane with a line passing through \( (0, -4) \) and \( (1, 0) \) — does not match.
- A coordinate plane with a line passing through \( (-4, -2) \), \( (0, -1) \), and \( (4, 0) \) — does not match.
- A coordinate plane with a line passing through \( (-2, -4) \), \( (-1, 0) \), and \( (0, 4) \) — does not match.
- A coordinate plane with a line passing through \( (-4, 0) \) and \( (0, 1) \) — matches.
Thus, the correct choice is the last option, which represents the line for the equation \( x - 4y = -4 \).
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