Question

fill in the missing numbers to complete the linear equation that gives the rule for this table.

x	1	2	3	4
y	18	36	54	72

y = \boxed{}x + \boxed{}

Explanation:

Step1: Find the slope (coefficient of x)

We use two points \((x_1, y_1) = (1, 18)\) and \((x_2, y_2) = (2, 36)\). The slope \(m\) is calculated as \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{36 - 18}{2 - 1}=\frac{18}{1}=18\).

Step2: Find the y - intercept (constant term)

Using the point - slope form \(y=mx + b\) and the point \((1,18)\) with \(m = 18\). Substitute \(x = 1\), \(y = 18\) and \(m = 18\) into the equation: \(18=18\times1 + b\). Solving for \(b\), we get \(b=18 - 18=0\). So the equation is \(y = 18x+0\).

Answer:

\(y=\boxed{18}x+\boxed{0}\)