choose the correct solution and graph the inequality
y/3>-5
To graph the inequality \( y/3 > -5 \), first, we need to isolate \( y \) by multiplying each side of the inequality by 3:
\( y > -5 \times 3 \)
This leads to:
\( y > -15 \)
The solution to the inequality is all \( y \)-values greater than -15. To graph this inequality, we would follow these steps:
1. Draw a coordinate plane with a y-axis and an x-axis.
2. Locate -15 on the y-axis.
3. Since the inequality is strictly greater than (>) and not greater than or equal to (≥), we use a dashed horizontal line at y = -15 to indicate that the line itself is not part of the solution.
4. Shade the region above the dashed line because we want all \( y \)-values that are greater than -15. This shaded region represents all ordered pairs (x, y) where y is greater than -15.
Here is a basic representation of this graph:
```
|
|
| (Shaded Region)
|........> y = -15
|
|________________________
```
The dashed line represents y = -15, and the arrow indicates that the region above that line is shaded, encompassing all \( y \)-values greater than -15 regardless of \( x \)-values.