Question

Is the function in the table linear or nonlinear and why? x y 0,−100 and 1,-50 and 2,0 and 3,100 and 4,150. (A)The function is not linear because there are negative values in the y values. (b) The function is linear because the y values are multiples of 50. (c) The function is not linear because the rate of change is not constant. (D) The function is linear because the x values increase by a constant number.

Answer 1

Answer:

The correct option is c.

Step-by-step explanation:

Linear function: The rate of change of a linear function is always constant.

Non-Linear function: The rate of change of a non-linear function is not constant.

From the given coordinate pairs it is noticed that the function is passing through the points (0,-100), (1,-50), (2,0), (3,100) and (4,150).

$m=\frac{y_2-y_1}{x_2-x_1}$

The slope of function for points (0,-100) and (1,-50) is

$m_1=\frac{-50-(-100)}{1-0}=50$

The slope of function for points (2,0) and (3,100) is

$m_2=\frac{100-0}{3-2}=100$

Since the slopes of function are different, therefore the given function is non-linear.

The function is not linear because the rate of change is not constant and option c is correct.

Answer 2

The answer should be B