To find the [tex]$y$[/tex]-intercept of the equation [tex]\( x + 5y = 20 \)[/tex], follow these steps:
### Step-by-Step Solution:
1. Understand the Concept of y-Intercept:
- The [tex]$y$[/tex]-intercept is the point where the graph of the equation crosses the [tex]$y$[/tex]-axis.
- At the [tex]$y$[/tex]-intercept, the value of [tex]$x$[/tex] is always [tex]$0$[/tex] because it lies on the [tex]$y$[/tex]-axis.
2. Set [tex]$x = 0$[/tex]:
- Substitute [tex]$x = 0$[/tex] into the equation [tex]\( x + 5y = 20 \)[/tex].
[tex]\[ 0 + 5y = 20 \][/tex]
3. Solve for [tex]$y$[/tex]:
- Isolate [tex]$y$[/tex] by dividing both sides of the equation by [tex]$5$[/tex].
[tex]\[ 5y = 20 \][/tex]
[tex]\[ y = \frac{20}{5} \][/tex]
[tex]\[ y = 4 \][/tex]
4. Identify the y-Intercept:
- Since [tex]$y = 4$[/tex] when [tex]$x = 0$[/tex], the [tex]$y$[/tex]-intercept is the point [tex]$(0, 4)$[/tex].
### Conclusion:
The [tex]$y$[/tex]-intercept of the graph of the equation [tex]\( x + 5y = 20 \)[/tex] is [tex]$4$[/tex].
Thus, the graph crosses the [tex]$y$[/tex]-axis at the point [tex]\((0, 4)\)[/tex].
