A line with slope 3 intersects a line with slope 5 at the point (10, 15). What is the distance between the I-intercepts of these two lines?​

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 intercepts:

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