To find the intercepts of the line given by the equation [tex]\( x + 2y = 10 \)[/tex], follow these steps:
### Finding the [tex]\( x \)[/tex]-intercept:
1. The [tex]\( x \)[/tex]-intercept occurs where the line crosses the [tex]\( x \)[/tex]-axis. At this point, the value of [tex]\( y \)[/tex] is 0.
2. Substitute [tex]\( y = 0 \)[/tex] into the equation:
[tex]\[ x + 2(0) = 10 \][/tex]
3. Simplify:
[tex]\[ x = 10 \][/tex]
4. Therefore, the [tex]\( x \)[/tex]-intercept is [tex]\( (10, 0) \)[/tex].
### Finding the [tex]\( y \)[/tex]-intercept:
1. The [tex]\( y \)[/tex]-intercept occurs where the line crosses the [tex]\( y \)[/tex]-axis. At this point, the value of [tex]\( x \)[/tex] is 0.
2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ 0 + 2y = 10 \][/tex]
3. Simplify:
[tex]\[ 2y = 10 \][/tex]
4. Solve for [tex]\( y \)[/tex]:
[tex]\[ y = \frac{10}{2} = 5 \][/tex]
5. Therefore, the [tex]\( y \)[/tex]-intercept is [tex]\( (0, 5) \)[/tex].
### Summary:
- The [tex]\( x \)[/tex]-intercept is: [tex]\( (10, 0) \)[/tex]
- The [tex]\( y \)[/tex]-intercept is: [tex]\( (0, 5) \)[/tex]
These are the ordered pairs representing where the line crosses the [tex]\( x \)[/tex]-axis and [tex]\( y \)[/tex]-axis, respectively.
