Question

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

x	4	5	6	7
y	0	1	2	3

y = \square x - \square

Explanation:

Step1: Find the slope (coefficient of x)

We use two points \((x_1,y_1)=(4,0)\) and \((x_2,y_2)=(5,1)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1 - 0}{5 - 4}=1\). So the coefficient of \(x\) is \(1\), so the equation is \(y = 1x - b\) (or \(y=x - b\)).

Step2: Find the y-intercept (b)

Use the point \((4,0)\) in \(y=x - b\). Substitute \(x = 4\), \(y = 0\): \(0=4 - b\). Solving for \(b\), we get \(b = 4\).

Answer:

\(y=\boxed{1}x-\boxed{4}\)