Answer:
To find the equation of the line that passes through the point (8, -5) and is perpendicular to the line 5x + 4y = 24, you can use the following steps:
Find the slope of the line 5x + 4y = 24. To do this, you can rearrange the equation to the slope-intercept form y = mx + b, where m is the slope. So, you get y = -5/4 x + 6
Since the line is perpendicular to the line 5x + 4y = 24, the slope of the line is the negative reciprocal of the slope of the line 5x + 4y = 24 which is -4/5
Now, use the point-slope form of the equation of a line which is y - y1 = m(x - x1). So, the equation of the line that passes through the point (8, -5) and is perpendicular to the line 5x + 4y = 24 is :
y - (-5) = -4/5(x - 8)
y + 5 = -4/5x + 8/5
y = -4/5x + 13/5
So, the equation of the line is y = -4/5x + 13/5