To find the coordinates where the line $y = 2x$ cuts the axes, we need to consider two points:

1. Intersection with the x-axis:

   • On the x-axis, $y = 0$.
   • Substitute $y = 0$ into the equation $y = 2x$:

   $0 = 2x$

   Solving for $x$, we get:

   $x = 0$

   So, the line intersects the x-axis at the point $(0, 0)$.

2. Intersection with the y-axis:

   • On the y-axis, $x = 0$.
   • Substitute $x = 0$ into the equation $y = 2x$:

   $y = 2(0) = 0$

   So, the line also intersects the y-axis at the point $(0, 0)$.

Thus, the line $y = 2x$ cuts both the x-axis and y-axis at the origin, with coordinates $(0, 0)$.

Would you like more details or have any questions? Here are some related questions:

1. How can you find the intersection points of two lines?
2. What happens if the line is vertical, like $x = 2$?
3. How do you determine the slope of a line from its equation?
4. What is the general method for finding intercepts in a quadratic equation?
5. How does the slope affect where a line intersects the axes?

Tip: Always remember that a line in slope-intercept form $y = mx + b$ intersects the y-axis at $(0, b)$, where $b$ is the y-intercept.