Question

1. if the points (1, 2), (2, 4), (3, 6), (4, 8) are plotted on a graph, what type of function do they represent?

a. undefined

b. linear

c. non - linear

d. they do not represent a function.

Explanation:

Step1: Check if it's a function

A relation is a function if each input (x - value) has exactly one output (y - value). For the points \((1,2)\), \((2,4)\), \((3,6)\), \((4,8)\), each \(x\) - value (1, 2, 3, 4) has a unique \(y\) - value (2, 4, 6, 8). So, it is a function. So option d is incorrect.

Step2: Check if it's linear

For a linear function, the slope between any two points should be the same. The slope \(m\) between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\).

• Slope between \((1,2)\) and \((2,4)\): \(m_1=\frac{4 - 2}{2 - 1}=\frac{2}{1} = 2\)
• Slope between \((2,4)\) and \((3,6)\): \(m_2=\frac{6 - 4}{3 - 2}=\frac{2}{1}=2\)
• Slope between \((3,6)\) and \((4,8)\): \(m_3=\frac{8 - 6}{4 - 3}=\frac{2}{1}=2\)

Since the slope between all pairs of consecutive points is the same (equal to 2), the function is linear. Option a is incorrect because the function is defined, and option c is incorrect because the function is linear.

Answer:

b. Linear