The **distance between the intercepts **of both lines is 2 units

The equation of a line in slope intercept form is:

Where:

slope

y intercept

For the first line, we have:

---- the slope

So, the equation of the first line is:

For the second line, we have:

--- the slope

So, the equation of the second line is:

Both lines intersect at (10,15) means that (10,15) is a common solution to the equation of both lines

i.e.

Substitute these values in the first equation and solve for b

So, the equation of the first line is

Repeat the same process for the second line

So, the equation of the second line is

The x intercept is when

So, we substitute 0 for y and solve for x in the equations of both lines

For line 1

---- Collect like terms

--- Divide both sides by 3

The x intercept of line 1 is 5

For line 2

--- Collect like terms

-- Divide both sides by 5

The x intercept of line 2 is 7

The distance (d) between both is the difference in the calculated intercepts: