The line with equation 7x + 5y = 70 intersects the x-axis and y-axis at A and B respectively

Given the line equation \( 7x + 5y = 70 \), we want to find the points where it intersects the x-axis and y-axis, denoted as points \( A \) and \( B \), respectively.

### Step 1: Find the x-intercept (Point \( A \))
- The x-intercept occurs when \( y = 0 \).
- Substitute \( y = 0 \) into the equation:
  \[
  7x + 5(0) = 70
  \]
  \[
  7x = 70
  \]
  \[
  x = \frac{70}{7} = 10
  \]
- Therefore, the point \( A \) where the line intersects the x-axis is \( A(10, 0) \).

### Step 2: Find the y-intercept (Point \( B \))
- The y-intercept occurs when \( x = 0 \).
- Substitute \( x = 0 \) into the equation:
  \[
  7(0) + 5y = 70
  \]
  \[
  5y = 70
  \]
  \[
  y = \frac{70}{5} = 14
  \]
- Therefore, the point \( B \) where the line intersects the y-axis is \( B(0, 14) \).

### Final Answer
The line \( 7x + 5y = 70 \) intersects:
- The x-axis at point \( A(10, 0) \).
- The y-axis at point \( B(0, 14) \).

Would you like any more details or have any questions?

Here are 5 related questions you might find interesting:
1. How do you find the distance between two points on a coordinate plane?
2. How can you find the midpoint of the line segment connecting points \( A \) and \( B \)?
3. What is the slope of the line \( 7x + 5y = 70 \)?
4. How do you determine the area of the triangle formed by the origin and points \( A \) and \( B \)?
5. How does changing the coefficients in the equation \( 7x + 5y = 70 \) affect the intercepts?

**Tip:** When finding intercepts, set one variable to zero and solve for the other to quickly identify where the line crosses the axes.

Learn how to find the x-intercept and y-intercept of the line equation 7x + 5y = 70. This problem covers coordinate geometry concepts, including intercepts and equations of lines. Suitable for students in Grades 9-12.

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