Question

The Tigers are playing a basketball game. In order to break a school record, they must score more than 105 points in the game. The team can either make a 2-point basket or a 3-point basket to score.

Which of the following graphs represents this situation?


J.
K.

L.
M.

Answer 1

To represent the situation of the Tigers needing to score more than 105 points using 2-point and 3-point baskets, we can set up an inequality based on the number of each type of basket they make.

Let:
- \( x \) = number of 2-point baskets made
- \( y \) = number of 3-point baskets made

The total points scored can be represented by the equation:
\[
2x + 3y > 105
\]

To graph the inequality \( 2x + 3y > 105 \):

1. First, convert the inequality to an equation to find the boundary line:
\[
2x + 3y = 105
\]

2. To find the intercepts:
- When \( x = 0 \):
\[
3y = 105 \implies y = 35
\]
- When \( y = 0 \):
\[
2x = 105 \implies x = 52.5
\]

3. Plot the points \( (0, 35) \) and \( (52.5, 0) \) on the graph.

4. The shaded area for \( 2x + 3y > 105 \) will be above this line since we're interested in scores greater than 105.

5. The boundary line itself should be dashed (not solid) since scores must be strictly greater than 105 (not equal to).

When evaluating the options (graphs J, K, L, M), look for a graph that:
- Shows a dashed line for the equation \( 2x + 3y = 105 \).
- Has the region above the dashed line shaded, indicating scores greater than 105.

If you have the graphs labeled J, K, L, M, refer to the one that matches these criteria.