Find the coordinates of the point where the line y= 2x cuts the axis.

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.

Learn how to find the intersection points of the line y=2x with the x-axis and y-axis. This problem involves linear equations and coordinate geometry, suitable for students in Grades 6-8. Explore the step-by-step solution to see how the line passes through the origin.

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