Final answer:
The equation of the line that contains the point (-1, -7) and is parallel to the line 4x + 5y = 9 is option C) y = -4x - 7.
Step-by-step explanation:
To find the equation of a line parallel to 4x + 5y = 9, we need to determine the slope of the given line. The given line can be rewritten in slope-intercept form (y = mx + b), where m is the slope. Rearranging the equation, we get y = -4/5x + 9/5. The slope of the line is -4/5.
Since the line we're looking for is parallel, it has the same slope. Now, using the point-slope form of a line (y - y₁) = m(x - x₁), where (x₁, y₁) is the given point (-1, -7), we substitute the values and simplify. The equation becomes y + 7 = -4/5(x + 1). Expanding and rearranging, we get y = -4x - 7, which matches option C.
In conclusion, the correct equation for the line parallel to 4x + 5y = 9 and passing through (-1, -7) is y = -4x - 7.