SOLUTION: The line y=-12/5 x+ 2 is exactly 3 units away from two other lines parallel to it. The distance, in units, between the y-intercepts of these two other lines is... A)12 3/4 B)10 2/

Algebra ->  Graphs -> SOLUTION: The line y=-12/5 x+ 2 is exactly 3 units away from two other lines parallel to it. The distance, in units, between the y-intercepts of these two other lines is... A)12 3/4 B)10 2/      Log On


   

Question 1132614: The line y=-12/5 x+ 2 is exactly 3 units away from two other lines parallel to it. The distance, in units, between the y-intercepts of these two other lines is...
A)12 3/4 B)10 2/3 C)14 1/5 D)15 3/5 E)13 5/6
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

The line y=-%2812%2F5%29+x%2B+2 is exactly 3 units away from two other lines parallel to it.
y=-%2812%2F5%29+x%2B+2...both sides multiply by 5
5y=-12+x%2B+10
12x+%2B+5y+-+10+=+0+

The distance from a point (x,+y) to a line ax+%2B+by+%2B+c+=+0 is given by
distance = ax+%2B+by+%2B+c%29%2Fsqrt%28a%5E2%2Bb%5E2%29+

You have the line
12x+%2B+5y+-+10+=+0+=>a=12,b=5,c=10

You want the distance from y-intercept point (0, y) to be 3.

%2812%2A0+%2B+5%2Ay+-+10%29%2Fsqrt%2812%5E2%2B5%5E2%29++=+3+
%285%2Ay+-+10%29%2Fsqrt%28169%29++=+3+
%285%2Ay+-+10%29%2F13+=+3+ ... multiply by 13
5%2Ay+-+10+=+39+
5%2Ay++=+39%2B10+
5%2Ay++=+49
y++=+49%2F5

This has two solutions:

+5y+-+10+=+39
+y+=+49%2F5+
And
+5y+-+10+=+-39+
+y+=+-29%2F5+

The difference of these two y-intercept values is
+49%2F5+-+%28-29%29%2F5+=+78%2F5+=+15.6+=>156%2F10=>153%2F5
answer: D)15+3%2F5