SOLUTION: Find the distance between the two lines. Line 1 y= 3/5x + 2 Line 2 Y= 3/5x - 1 Round to the nearest hundreth.

Algebra ->  Length-and-distance -> SOLUTION: Find the distance between the two lines. Line 1 y= 3/5x + 2 Line 2 Y= 3/5x - 1 Round to the nearest hundreth.       Log On


   

Question 1005617: Find the distance between the two lines.
Line 1 y= 3/5x + 2
Line 2 Y= 3/5x - 1
Round to the nearest hundreth.
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
Try to make use of the y-axis intercept of one of the equations. Find a linear equation perpendicular to these two parallel lines. Drawing the graphs on the three equations on the same coordinate system should give you a clearer idea of the strategy.

Does that help?
Here is a way to think through.
graph%28300%2C300%2C-4%2C4%2C-4%2C4%2C3x%2F5%2B2%2C3x%2F5-1%29


The line perpendicular to both of these and passing through (0,2) is y-2=-%285%2F3%29%28x-0%29, which when put into slope intercept form is y=-%285%2F3%29x%2B2; not surprising. This line intersects your line 1 and line 2.

graph%28300%2C300%2C-4%2C4%2C-4%2C4%2C3x%2F5%2B2%2C3x%2F5-1%2C-5x%2F3%2B2%29

What is the intersection point of line 2 and the line y=-%285%2F3%29x%2B2 perpendicular to it?
-%285%2F3%29x%2B2=%283%2F5%29x-1
-%285%2F3%29x-%283%2F5%29x=-1-2
%285%2F3%2B3%2F5%29x=3
multiply bothsides by lcd of 15,
25x%2B9x=45
34x=45
x=45%2F34
-
Now find y of the intersection
y=%283%2F5%29x-1
y=%283%2F5%29%2845%2F34%29-1
.
.
y=-7%2F34
-
The intersection of line 2 and the perpendicular is ( 45/34, -7/34).

Now, what is the distance between (0,2) and ( 45/34, -7/34 )?
Use the Distance Formula.