Answer:
6.7 units
Step-by-step explanation:
The shortest distance between two lines is the perpendicular line.
y = 2x + 3
Slope of the perpendicular line: - 1/2
Point (-5,8)
b (y-intersect) = 8 - (-1/2)(-5) = 11/2
Perpendicular line equation: y = -1/2x + 11/2
y = y
2x +3 = -1/2x + 11/2
2x + 1/2x = 11/12 - 3
5/2x = 5/2
x = (5/2) / (5/2)
x = 1
Plug x = 1 into any of the equations of the line to find y.
y = 2x + 3
y = (2*1)+3 = 5
Points from the perpendicular line (1,5) and (-5,8)
Distance between these two points:
d = sqrt[(-5-1)^2 + (8-5)^2]
= sqrt (6^2 + 3^2) = sqrt 45
= 6.7
