In the coordinate plane, line m passes through the origin and has a slope of 3. If points (6, y) and (x, 12) are on line m, then y - x = ?

Question: In the coordinate plane, line m passes through the origin and has a slope of 3. If points (6, y) and (x, 12) are on line m, then y - x = ?

Solution:
Since the line passes through the origin (0, 0) and has a slope (m) of 3, we use the slope-intercept form y = mx + c.
Here, c = 0 and m = 3.
So, the equation of the line is y = 3x.

Now,
The point (6, y) is on the line.
Substituting x = 6 in the equation:
∴ y = 3 × 6
⇒ y = 18

Again,
The point (x, 12) is on the line.
Substituting y = 12 in the equation:
∴ 12 = 3x
⇒ x = 12/3
⇒ x = 4

Now, we need to find the value of y - x:
∴ y - x = 18 - 4
⇒ y - x = 14

∴ The value of y - x is 14.