# Thread: Slope-Intecept Form X-Intercept distance

1. ## Slope-Intecept Form X-Intercept distance

A line with slope 2 intersects a line with slope 6 at the point (40,30). What is the
distance between the x-intercepts of these lines? How is the answer 10?

2. Here is the way I would do it.
y=2x+b
30=2(40)+b
30=80+b
-50=b
y=2x-50

then y=6x+b
30=6(40)+b
30=240+b
-210=b
y=6x-210

we have y=2x-5 and y=6x-210
0=2x-5 and 0=6x-210
5=2x 210=6x
x=5/2 x=35
total answer of 32.5 but it is supposed to be 10 what am i doing wrong?

3. Originally Posted by sundance240
A line with slope 2 intersects a line with slope 6 at the point (40,30). What is the distance between the x-intercepts of these lines? How is the answer 10?
Suppose that (a,0) is the x-intercept of the line with slope 2.
Suppose that (b,0) is the x-intercept of the line with slope 6.
Now use the slope formula: 30/(40-a)=2 & 30/(40-b)=6.
Solve for a & b.

4. Hello, sundance240!

A silly error . . .

Here is the way I would do it.

y .= .2x + b
. . 30 .= .2(40) + b . . b = -50
. . y .= .2x - 50

y .= .6x + b
. . 30 .= .6(40) + b . . b =-210
. . y .= .6x - 210

. . . . . . . . . . . . . . .
We have: .y .= .2x - 5 . . . y .= .6x - 210