Final answer:
To find the equation of a line parallel to 5x + 4y = 24 and passing through (8, -5), first find the slope of the given line. The slope is -5/4. Use this slope to construct the equation of the parallel line. The equation is y = (-5/4)x - 15.
Step-by-step explanation:
To find the equation of a line parallel to the given line and passing through the point (8, -5), we need to determine the slope of the given line and use that slope to construct the equation of the parallel line.
The given line has the equation 5x + 4y = 24. To find its slope, we need to rearrange the equation in the form y = mx + b, where m represents the slope.
In this case, by isolating y, we have y = (-5/4)x + 6.
Since the parallel line will have the same slope as the given line, the equation of the parallel line passing through (8, -5) is y = (-5/4)x + b.
To find the value of b, we substitute the coordinates of the given point into the equation. Plugging in (8, -5), we have -5 = (-5/4)(8) + b.
Solving for b, we get b = -15.
Therefore, the equation of the line that passes through (8, -5) and is parallel to 5x + 4y = 24 is y = (-5/4)x - 15.