math word problem, please help me out!!!!thanks?

Question

a line with slope 3, intersects a line with a slope 5 at the point (10,15). what is the distance between the x-intercepts of these two lines?
please show work, of how to arrive at answer
thanks in advance for your help! ~USA~

Answer 1

The general equation for a line is

y = mx + b

where m is the slope.

Line 1 has equation y = ( 3 ) x + b and passes through ( 10, 15 ) so (15 ) = ( 3 ) ( 10 ) + b -> b = -15

Line 1: y = 3x - 15

Line 2 has equation y = ( 5 ) x + b and passes through ( 10, 15 ) so ( 15 ) = ( 5 ) ( 10 ) + b -> b = -35

Line 2: y = 5x - 35

Now find their x-intercepts. These occur at y = 0:

Line 1: 0 = 3x - 15 -> x = 5
Line 2: 0 = 5x - 35 -> x = 7

The distance between these points is 2.

Answer 2

Get a piece of graph paper and graph a point at (10.15). Then draw a line from there with slope of 3 (in other words, you go down 3 and over 1). Do the same for a line of slope 5. Measure the distance between the points where these lines cross the x-axis.

Answer 3

y=5x + b, so 15 = 50+b --> b = -35 [1st line]
y=3x +b, so 15 = 30+b --> b = -15 [2nd line]
When y = 0 x = 7 [first line]
When y= 0, x = 5 [second line]
Thus distance is 7-5 = 2

Answer 4

i drew it up and got 2