Label each line as line 1: y=-2x+1 & line 2: y=-2x+16. The slopes of 2 lines are equal: n=-2, so they are parallel to each other. Line 1 & line 2 intersect y-axis at P(0,1) & Q(0,16), and x-axis at R(0.5,0) & S(8,0) respectively. Therefore the vertical distance for any x value is 15 (=PQ), and the horizontal dist. for any y value is 7.5 (=RS).
Since 2 lines are parallel, the shortest distance is obtained when it's measured perpendicularly to them. Label a line, that passes thru P(0,1) & intersects line 2 perpendicularly at T, as line 3: y=mx+1. By definition of line 3, the slope of line 3, m, is the negative reciprocal of the slope of line 2: n=2. ⇒ m=-(1/n)=-(1/-2) ⇔ m=1/2 So line 3 is rewritten as follows: y=½·x+1
The coordinates of T are obtained by solving equations of line 2 & line 3. -2x+16=½·x+1 ⇒ x=6, y=4 ⇒ T(6,4) By the Pythagorean theorem, PT²=(6－0)²+(4－1)² ⇒ PT=3√5 (= approx. 6.7082) Therefore, vertical dist.=15, horizontal dist.=7.5, & perpendicular dist.=3√5.