How can Kendra determine if the function is actually linear?

Mathematics

2 answers:

pashok25 [27]3 years ago

8 0

Answer:

D. She can check to see if the rate of change between the first two ordered pairs is the same as the rate of change between the first and last ordered pairs.

Step-by-step explanation:

Find the rate of change between first two ordered pairs and the second two ordered pairs:

1. Points (2,4) and (3,9). Rate of change:

$\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9-4}{3-2}=\dfrac{5}{1}=5$

2. Points (3,9) and (4,16). Rate of change:

$\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{16-9}{4-3}=\dfrac{7}{1}=7$

The rate of change for the linear function must the same for each two points on the graph of the function. In this case, the reate of change differs, so this function is not linear and correct option is D.