The equation of the line is: y = -3/5x + 1.
How to Write the Equation of a Line?
The slope (m) of two lines that lie perpendicular to each other are negative reciprocals.
Given, y = 5/3x - 3, the slope (m) of the line is 5/3. The negative reciprocal of 5/3 is -3/5.
Thus, the line that is perpendicular to it will have a slope (m) of -3/5.
Substitute m = -3/5 and (a, b) = (5, -2) into y - b = m(x - a):
y - (-2) = -3/5(x - 5)
y + 2 = -3/5x + 3
y + 2 - 2 = -3/5x + 3 - 2
y = -3/5x + 1
Thus, the equation of the line is: y = -3/5x + 1.
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