Final answer:
The equation of the line that passes through the point (-5, -4) and is parallel to y = 3/5x + 5 is y = 3/5x - 1. This is found by using the point-slope form of a line equation with the given point and the slope, which is the same for parallel lines.
Step-by-step explanation:
To find the equation of a line that goes through the point (-5, -4) and is parallel to the equation y = 3/5x + 5, we first note that parallel lines have the same slope.
The slope of the line we want to find is therefore 3/5, the same as the slope of the given line.
Using the point-slope form of a line's equation, which is y - y1 = m (x - x1), where (x1, y1) is a point on the line and m is the slope, we substitute our point and slope into the formula.
The point-slope form with our point and slope is y + 4 = 3/5(x + 5).
Simplifying this, we get y + 4 = 3/5x + 3.
Subtracting 4 from both sides, we find the equation of our parallel line: y = 3/5x - 1.