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.

Question 1132638: 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.
Found 2 solutions by MathLover1, Boreal:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
The line is exactly units away from two other lines parallel to it.
...both sides multiply by

The distance from a point (,) to a line is given by
distance =

You have the line
=>,,

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

... multiply by 13

This has two solutions:

And

=> two other lines parallel to given line are:
and

In the graphic, the radius of the circle is , showing the distance to the other two lines is .

The difference of these two y-intercept values is
=>=>
answer: D)

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The slope of the line is -12/5, and the slope of the line perpendicular to that is 5/12.

this is the general form of the line perpendicular to the given line.
We want to go 3 units out on the perpendicular.
Suppose the perpendicular is to the line at the x-intercept of (5/6, 0). Then the line can be shown using the point slope formula of y-y1=m(x-x1), where m is slope and (x1, y1) are (5/6, 0) to be y=(5/12)x-(25/72)

Going to the right 3 units is a right triangle with the line 3 units away. The length of the hypotenuse is where the x-intercept is for that line. The angle for a slope of 5/12 is where the tangent of an angle is 5/12, which is arc tan (5/12) or 22.62 degrees.
So cos 22.62 =3/hypot
hypot=3/cos 22.62=3.25 units away from (5/6, 0) so the x-intercept of that line is 3.25+5/6 or (4.08, 0)
We know the slope of this parallel line is -2.4, and we have a point, so the equation of the line is y=-2.4(x-4.08)=y=-2.4x+9.08.

The distance to the x-intercept in the other direction is -3.25 units, so the x-intercept is at -3.25+5/6=-2.42 or (-2.42, 0)
The equation of this line is y=-2.4(x+2.42)=-2.4x-5.8

The distance between the two y-intercepts is 9.08-(-5.8)=14.88 units ANSWER

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