Answer:
The equation of the line that passes through the point (-5, 5) and is parallel to the line x + 5y = 25 is y = -1/5x + 4.
Explanation:
1. Convert the given equation x + 5y = 25 into slope-intercept form (y = mx + b).
Start by isolating y:
x + 5y = 25
5y = -x + 25
y = (-1/5)x + 5
From this equation, the slope of the line is -1/5.
2. Parallel lines have the same slope. So, the slope of the desired line is also -1/5.
3. Now, use the slope-intercept form (y = mx + b) and substitute the values of the given point (-5, 5) and the slope (-1/5) to find the value of b.
y = -1/5x + b
5 = (-1/5)(-5) + b
5 = 1 + b
b = 4
4. Finally, the slope (-1/5) and the y-intercept (b = 4). We can combine these values to form the equation of the line:
y = -1/5x + 4
Therefore, the equation of the line that passes through the point (-5, 5) and is parallel to the line x + 5y = 25 is y = -1/5x + 4.