Answer:
[tex]y = -\frac{1}{5}x + 7[/tex]
Step-by-step explanation:
Perpendicular lines are lines which intersect at a 90 degree angle. They also are lines which slopes are negative reciprocals of each other. The line y = 5x + 3 has slope 5 and the negative reciprocal is -1/5. Substitute m = -1/5 and the point (5,6) into the point slope form. Then convert using the distributive property and inverse operations.
[tex]y - y_1 = m(x-x_1)\\y - 6 = -\frac{1}{5}(x - 5)\\y - 6 = -\frac{1}{5}x + 1\\y = -\frac{1}{5}x + 7[/tex]
