Question

Kiana created a table of points. Explain whether Kiana has demonstrated a proportional relationship.

x
y

2
25

4
50

6
75
PLEASE HELP

Answer 1

Kiana has demonstrated a proportional relationship.

The data is linear.

The line passes through the origin.

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Step-by-step explanation

Divide each y value over each x value for each separate row.

`\begin{array}c \cline{1-3}\text{x} & \text{y} & \text{y}/\text{x}\\\cline{1-3}2 & 25 & 12.5\\\cline{1-3}4 & 50 & 12.5\\\cline{1-3}6 & 75 & 12.5\\\cline{1-3}\end{array}`

We get the same result each time, which tells us that Kiana has demonstrated a proportional relationship.

The value of k is k = 12.5 which means y/x = k leads to y = kx

The equation for her points is y = 12.5x

For instance, if x = 2 then y = 12.5*2 = 25.

Because the data is proportional, it is a linear equation that passes through the origin. The slope is 12.5 and the y intercept is 0.