Question

The equation of the line R1 is 2x +y-8=0. The line R2 is perpendicular to R1.
a. Calculate the gradient of R2.
b. The point of intersection of R1 and R2 is (4,k).
Find.
1. the value of k
2. the equation of R2

Answer 1

2x +y-8=0
is
y = (-2) x + 8
slope of R1 = m = -2
yaxis intercept at (0,8)
slope of R2 = -1/m = -1/-2 = +1/2
so
for R2, y = (1/2) x + b
hit at (4,k)
k = (1/2)4 + b
or k = 2 + b
k = -2 (4) + 8 = 0
so hit at (4,0)
0 = (1/2)4 + b
b = -2
so R2 is
y = (1/2) x - 2
check=========================
for R1 y = -2x+8
for R2 y = (1/2) x -2
--------------------------subtract
0 = -2.5 x + 10
so x = 4
y = -2(4) + 8 = 0 yes