Final answer:
The equation of the line passing through (-2, -7) that is parallel to 3x + 5y = 11 is y + 7 = (-3/5)(x + 2).
Step-by-step explanation:
To find the equation of the line passing through (-2, -7) that is parallel to 3x + 5y = 11, we need to determine its slope and y-intercept. Since the given line is in the form Ax + By = C, we can rewrite it as y = (-A/B)x + (C/B). Comparing this equation to 3x + 5y = 11, we can see that the slope of the given line is -A/B = -3/5.
The slope of any line parallel to the given line will also be -3/5. Using the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can substitute the values (-2, -7) and -3/5 for m to get the equation of the parallel line. Hence, the equation of the line passing through (-2, -7) that is parallel to 3x + 5y = 11 is:
y + 7 = (-3/5)(x + 2)