find the distance bewteen the parallel line y=-2/3x+8 and. the passes through (0,0)

Answer 1

Second line is y = - 2/3x.

Let (0, 8) is y-intercept of first line

Normal equation of second line is (2x + 3y)/√13 = 0.

So distance between lines d = I2·0 + 3·8I/√13 = 24/√13

Answer 2

the distance between (x₀,y₀) and line y=mx+b is it can be shown

d=|mx₀+b-y₀|/√(1+m²)

for this problem

d=8/√(13/9)

=(24√13)/13