SOLUTION: The line y=-12/5 x+2 is exactly 3 units away from two other parallel to it. The distance, in units, between the y-intercepts of these two line is A)12 3/4 B)10 2/3 C)14 1/5 D)15 3

Algebra ->  Graphs -> SOLUTION: The line y=-12/5 x+2 is exactly 3 units away from two other parallel to it. The distance, in units, between the y-intercepts of these two line is A)12 3/4 B)10 2/3 C)14 1/5 D)15 3      Log On


   

Question 1132637: The line y=-12/5 x+2 is exactly 3 units away from two other parallel to it. The distance, in units, between the y-intercepts of these two line is
A)12 3/4 B)10 2/3 C)14 1/5 D)15 3/5 E)13 5/6
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


By symmetry, the y-intercepts of the two lines will be the same distance from the y-intercept of the given line, 2. So find the distance from y=2 to the y-intercept of one of the two lines and double that distance.

Let A (0,2) be the y-intercept of the given line; let B(0,b) be the y-intercept of one of the two lines parallel to the given line and 3 units from it.

Let C be the point on the given line that is 3 units from B.

Then ACB is a right triangle. Since the slope of the given line is -12/5, the ratio of the lengths of AC and BC is 12:5. Since those are the legs of a right triangle, AB (the length we need to find) is the hypotenuse of a 5:12:13 right triangle.

Then, since BC is the short leg of the triangle, AB is (13/5)*3 = 39/5 = 7.8.

And so the distance between the y-intercepts of the two lines parallel to y = -12/5x+2 and 3 units from it is 2*7.8 = 15.6 = 15 3/5, answer D.