Question

Find the x and y-intercepts of the following equation:
5x + 2y = 10
•x-intercept (5, 0)
x-intercept (2,10) y-intercept (0, 5) y-intercept (0,2)

Answer 1

To find the x-intercept and y-intercept of the equation \( 5x + 2y = 10 \), we can follow these steps:

### Finding the x-intercept:
The x-intercept occurs where \( y = 0 \).

Substituting \( y = 0 \) into the equation:
\[
5x + 2(0) = 10
\]
\[
5x = 10
\]
\[
x = \frac{10}{5} = 2
\]

Thus, the x-intercept is \( (2, 0) \).

### Finding the y-intercept:
The y-intercept occurs where \( x = 0 \).

Substituting \( x = 0 \) into the equation:
\[
5(0) + 2y = 10
\]
\[
2y = 10
\]
\[
y = \frac{10}{2} = 5
\]

Thus, the y-intercept is \( (0, 5) \).

### Summary:
- The x-intercept is \( (2, 0) \).
- The y-intercept is \( (0, 5) \).

From the options provided, the correct intercepts are:
- x-intercept: \( (2, 0) \)
- y-intercept: \( (0, 5) \)