To derive the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) using the two points given: \( A(0, 4) \) and \( B(1, -1) \).
The formula for the slope (m) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Assigning the points:
- \( (x_1, y_1) = (0, 4) \)
- \( (x_2, y_2) = (1, -1) \)
Now substitute the values into the formula:
\[ m = \frac{-1 - 4}{1 - 0} = \frac{-5}{1} = -5 \]
Next, we can use one of the points to find the y-intercept (b). We'll use point \( A(0, 4) \):
In the slope-intercept form \( y = mx + b \):
- When \( x = 0 \), \( y = 4 \)
- Thus, \( b = 4 \)
Now we have:
- Slope \( m = -5 \)
- Y-intercept \( b = 4 \)
Putting these into the slope-intercept form gives us:
\[ y = -5x + 4 \]
However, the options you provided do not include this equation, and you mentioned options like:
- \( 3x - y = 4 \)
- \( y = 3x + 4 \)
- \( y = -3x - 4 \)
- \( y = 3x - 4 \)
Since the derived slope was negative, it's possible that an error occurred in interpreting the data or in option selection. Based on the points calculated, the slope of the line between the points (0, 4) and (1, -1) was indeed negative (-5).
For your question, you should double-check the graph and points. If using the calculated values, rewrite and match against your given options considering potential errors in representation.
If there’s a need for the closest match or clarification in the provided options, please let me know!