Answer:
[tex]y = -\frac{11}{2}x - 23[/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 UV has slope 2/11. This is found using the slope formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{1--1}{7--4}= \frac{2}{11}[/tex]
Since it will be perpendicular the slope is -11/2. Substitute m = -11/2 and the point (-4,-1) into the point slope form.
[tex]y - y_1 = m(x-x_1)\\y - -1 = -\frac{11}{2}(x - -4)\\y +1 = -\frac{11}{2}(x + 4)\\y + 1 = -\frac{11}{2}x - 22\\y = -\frac{11}{2}x - 23[/tex]
