Final answer:
To find the equation of a line that is parallel to the given line and passes through the point (-5, 4), we can use the point-slope form of a linear equation.
Step-by-step explanation:
To find the equation of a line that is parallel to the line 3x + 5y = 35 and passes through the point (-5, 4), we need to use the fact that parallel lines have the same slope. The given line has a slope of -3/5, so the parallel line will also have a slope of -3/5.
We can use the point-slope form of a linear equation to find the equation of the parallel line. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values (-5, 4) for (x1, y1) and -3/5 for the slope, we get the equation:
y - 4 = (-3/5)(x + 5)
Simplifying this equation gives us the final equation:
y = -3/5x + 17/5