determine whether the given function is linear or nonlinear. if it is linear, determine the slope. is the…
determine whether the given function is linear or nonlinear. if it is linear, determine the slope. is the function a linear function? yes no determine the slope. select the correct choice below and fill in any answer boxes within your choice. a. the slope of the function is b. the function is not linear.
Answer
Explanation:
Step1: Calculate the slope between consecutive points
The formula for slope (m=\frac{y_2 - y_1}{x_2 - x_1}). For ((x_1 = 0,y_1=-1)) and ((x_2 = 1,y_2 = 4)), (m_1=\frac{4-(-1)}{1 - 0}=\frac{4 + 1}{1}=5). For ((x_1 = 1,y_1 = 4)) and ((x_2 = 2,y_2 = 9)), (m_2=\frac{9 - 4}{2 - 1}=\frac{5}{1}=5). For ((x_1 = 2,y_1 = 9)) and ((x_2 = 3,y_2 = 14)), (m_3=\frac{14 - 9}{3 - 2}=\frac{5}{1}=5). For ((x_1 = 3,y_1 = 14)) and ((x_2 = 4,y_2 = 19)), (m_4=\frac{19 - 14}{4 - 3}=\frac{5}{1}=5).
Step2: Check if the slopes are equal
Since (m_1=m_2=m_3=m_4 = 5), the function is linear.
Answer:
Yes, the function is linear. The slope of the function is (5), so the correct choice is A. The slope of the function is (5).