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: \( (0, 5) \)