https://file.aiquickdraw.com/mathbot/file/1725807549516qr4xbbaq.jpg

The image presents the following problem:

The equation of the line \( l \) is:
\[
3x - y - 10 = 0
\]

We are asked to find the coordinates of the points where the line cuts the x-axis and y-axis.

### 1. Finding where the line cuts the x-axis:
At the x-axis, \( y = 0 \).

Substitute \( y = 0 \) into the equation of the line:
\[
3x - 0 - 10 = 0
\]
\[
3x = 10
\]
\[
x = \frac{10}{3}
\]

So, the point where the line cuts the x-axis is:
\[
\left( \frac{10}{3}, 0 \right)
\]

### 2. Finding where the line cuts the y-axis:
At the y-axis, \( x = 0 \).

Substitute \( x = 0 \) into the equation of the line:
\[
3(0) - y - 10 = 0
\]
\[
-y - 10 = 0
\]
\[
y = -10
\]

So, the point where the line cuts the y-axis is:
\[
(0, -10)
\]

### Final Answer:
- The x-axis intercept is \( \left( \frac{10}{3}, 0 \right) \).
- The y-axis intercept is \( (0, -10) \).

Would you like further details or clarifications? 

Here are 5 related questions to explore this concept:
1. How can you find the slope of the line from its equation?
2. What is the general form of the equation of a line, and how can it help in finding intercepts?
3. How can the distance between two intercepts on the axes be calculated?
4. What happens to the intercepts when the line's slope is zero or undefined?
5. How do parallel lines affect their intercepts?

**Tip:** When finding intercepts, always substitute zero for the other variable—this simplifies the calculation!

The equation of the line l is 3x - y - 10 = 0. Find the coordinates of the points where the line cuts the axes (x-axis and y-axis).

Learn how to find the x-axis and y-axis intercepts of the line equation 3x - y - 10 = 0. This problem involves key concepts in linear equations and coordinate geometry, suitable for Grades 8-10 students.

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