Final answer:
To find the equation of a line that is perpendicular to the given line, we need to determine the negative reciprocal of the slope of the given line. The given line has a slope of 5/2, so the negative reciprocal is -2/5.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the given line, we need to determine the negative reciprocal of the slope of the given line. The given line has a slope of 5/2, so the negative reciprocal is -2/5.
Next, we can use the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope we found. Plugging in the values (-5, -3) for (x1, y1) and -2/5 for m, we get y + 3 = -2/5(x + 5).
Simplifying the equation gives us the slope-intercept form y = -2/5x - 13/5.