Question

line segment ab has a slope 5/4 and contains point a(8,-7). what is the y-coordinate of point q(3,y) if qa is perpendicular to line ab? answer choices: a: y=-2 b: y=-3 c: y=1 d: y=3

Answer 1

u have a slope of 5/4...a perpendicular line will have a negative reciprocal slope...which means, the slope we need is -4/5.

Now we use y = mx + b
slope(m) = -4/5
(8,-7)
-7 = -4/5(8) + b
-7 = -32/5 + b
-7 + 32/5 = b
-35/5 + 32/5 = b
-3/5 = b

equation is : y = -4/5x - 3/5.....4x + 5y = -3

4x + 5y = -3....when x = 3
4(3) + 5y = -3
12 + 5y = -3
5y = -3-12
5y = - 15
y = -15/5
y = - 3 <===