Question

The graph shows the relation between the number of lightbulbs in the lighthouse and the distance from the port where the lighthouse is visible.

Interpret the graph and choose the correct conclusions from the graph.

• A. More the number of lightbulbs in the lighthouse less is the distance up to which it is visible.
• B. The equation of the given graph is y = x + 2.
• C. Both A and C
• D. The distance from the port where the lighthouse is visible when the number of lightbulbs is 16 is 18 feet.

Answer 1

The correct option is C Both A and C

$\begin{array}{ccccc}\text{Number of lightbulbs, x}& 0& 10& 12& 15\\ \text{Distance (in feet), y}& 2& 12& 14& 17\\ & (2=0+2)& (12=10+2)& (14=12+2)& (17=15+2)\end{array}$
The graph shows the relationship between the distance from the port where the lighthouse is visible (in feet), y, and the number of lightbulbs in the lighthouse, x. Each value in the distance, y, is obtained by adding 2 to the corresponding number of lightbulbs, x.
Hence, the equation for the relation shown in the graph is y = x + 2.
Option A is correct.
As the number of lightbulbs is increasing, the distance from the port where the lighthouse is visible is also increasing.
Option B is incorrect.
The distance from the port where the lighthouse is visible when the number of lightbulbs is 16 is obtained by putting x = 16 in the equation y = x + 2.
Distance = 16 + 2 = 18 feet
Option C is correct.
Hence, option D is correct.