To determine a viable solution based on the graph provided in your description, we need to analyze the line connecting the points (0, 20) and (15, 0). This line represents the maximum number of adults and children that can be present at the party, leading to an equation we can derive from these endpoints.
Deriving the equation of the line:
-
Find the slope (m) of the line:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 20}{15 - 0} = \frac{-20}{15} = -\frac{4}{3}
\]
-
Use the point-slope form of the line equation (using point (0, 20)):
\[
y - 20 = -\frac{4}{3}(x - 0)
\]
\[
y = -\frac{4}{3}x + 20
\]
The inequality representing the possible number of adults (x) and children (y) in attendance typically will be of the form:
\[
y \leq -\frac{4}{3}x + 20
\]
Analyzing the problem:
To find a viable solution in the context of the party, a point (x,y) must fall on or below the line and must fall within the bounds of the axes (i.e., \(x \geq 0\) and \(y \geq 0\)).
Example of valid points:
Select points within the valid region (below the line and above the axes):
- (0, 0): This is at the origin and represents no adults and no children.
- (5, 10): Substitute in the line equation:
\[
y = -\frac{4}{3}(5) + 20 = -\frac{20}{3} + 20 = \frac{40}{3} \approx 13.33
\]
This point is below the line.
- (10, 5): Substitute in the line equation:
\[
y = -\frac{4}{3}(10) + 20 = -\frac{40}{3} + 20 = \frac{20}{3} \approx 6.67
\]
This point is also below the line.
You can select any of the above valid points or similar ones.
Answer format:
Let's choose (5, 10) for the response. Thus, you can enter:
(5,10)
If you have specific points you would like to check or other options, please let me know!
1 answer