Answer:
31
Explanation:
To find the equation of the line parallel to the line with slope m = 3/2 and passing through the point (5, -8), we can follow these steps: 1. Recall that parallel lines have the same slope. Since the given line has a slope of m = 3/2, the line we are looking for will also have a slope of 3/2. 2. Use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. 3. Substitute the values into the equation. In this case, we have x1 = 5, y1 = -8, and m = 3/2. So, the equation becomes y - (-8) = (3/2)(x - 5). 4. Simplify the equation. Distribute 3/2 to (x - 5): y + 8 = (3/2)x - (15/2). 5. To make the equation easier to work with, we can multiply all terms by 2 to eliminate the fraction: 2y + 16 = 3x - 15. 6. Rearrange the equation to the standard form, which is Ax + By = C. Move 3x to the left side and 16 to the right side: 3x - 2y = 31. Therefore, the equation of the line parallel to the line with slope m = 3/2 and passing through the point (5, -8) is 3x - 2y = 31.