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Find the intercepts for [tex]$x + 2y = 10$[/tex]. Make sure you write your answers as ordered pairs (a, b).

The [tex]$x$[/tex]-intercept is: [tex]\square[/tex]

The [tex][tex]$y$[/tex][/tex]-intercept is: [tex]\square[/tex]

Sagot :

GinnyAnsweridn
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.
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