VERY HARD.How do I find the distance between y=2x+2 and y=2xminus3?

Question

steps if possible.

Answer 1

graph both lines and find x-intercepts
then use the distance formula

Answer 2

Well, first of all you need to note that the slopes of both the lines are the same. That is, since the formula y=mx+b has the same value for m (2) in both cases, the lines are parallel, and the distance between them is a constant and does not depend on the value of x.

There are a couple of ways to find the distance between the two lines. First, you could write a formula for the distance between any single point on the first line and each of the points on the second. Then you could take the derivative of the distance and find the place that derivative is zero.

Pick a point on the first line, say (0,2)
The distance between any point on the second line (x, 2x-3) and (0,2) is
d(x) = sqrt(x^2 + (5-2x)^2)
= (5x^2 - 10x + 25)^1/2
the derivative of this is
d'(x) = (5x^2 - 10x + 25)^(-.5) * (10x - 10)
which is zero only when 10x = -10, or x = 1

So, the distance is a minimum from (0,2) when the point on the second line is (1, -1)

So, the distance in this case is sqrt(1^2 + 3^2) = sqrt(10)

Answer 3

The distance between the two functions is 5.

Since you have the same x-variable (2x), you just need to find the distance between the remaining parts of the equations.

2-(-3)=5

You can test it by plugging in some points for x.

For example

x=0, y =2, -3 ----->Distance = 5
x=1, y=4, -1 ------>Distance = 5

Answer 4

If I'm correct, the distance is between parallel lines. If they're not parallel, I don't know how to find it, but if they are, it's easy.

Remember that distance is ALWAYS measured on perpendiculars. So, using what you know about lines, make a line that is perpindicular to the preexisting two. It's formula is (y-y1) = m(x-x1) where (y1, x1) is the coordinates of a point on one of the lines. M is the new line's slope, which is the reciprocal of the previous two.

Using that new line, you now have two points to work with - one on each of your original two lines. This will go into your distance formula, which is as follows:

Distance is the square root of the whole line below

(x2-x1)^2 +(y2-y1)^2

^2 means squared.

(x1,y1) is the coordinate of the point on the first line. (x2, yx2) is the chosen cordinate on the second. Plug them into your formula and voila.

The distance between the lines.

Answer 5

These are two lines with the same slope, which is x. And the only difference between them is the +2 and -3 offsets which move the two lines away from the 0 intercept.

Answer 6

Graph both points and then find the slope between the two equations.