Supposed the line “L” is parallel to the line y=3/4x+6 and four units away from it. Which of the following is a possible equation of line “L”?

Question

a) y=3/4x

b) y=3/4x+1

c) y=3/4x+2

d) y=3/4x+3

e) y=3/4x+9/2

Answer 1

b) y=(3/4)x + 1

this line has a vertical distance from y=(3/4)x+6 of 5. 6-1=5. But the distance of a perpendicular connecting the two lines is less than 5, probably 4

the perpendicular line intersecting b) y=(3/4)+1 is y=-(4/3)x+1, crossing the parallel line at (0,1) and crossing the original line at (-12/5,21/5) use the distance formula d^2 = difference in x's squared + difference in y's squared to calculate the distance between those 2 points

d = sqr(144/25 + 256/25) = (1/5)sqr(144+256) = (1/5)sqr400 = 20/5 = 4

5 (6-1) is the hypotenuse of a right triangle with sides 3 and 4. 4 is the distance between the 2 parallel lines. 3 is the distance from the intersection point to (0,6)