Question

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

x	y
3	48
4	47
5	46

( y = square x + square )

Explanation:

Step1: Find the slope (m)

The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take the points \( (2, 49) \) and \( (3, 48) \). Then \( m=\frac{48 - 49}{3 - 2}=\frac{- 1}{1}=-1 \).

Step2: Find the y - intercept (b)

We use the slope - intercept form of a linear equation \( y = mx + b \). We know \( m=-1 \) and we can use the point \( (2, 49) \). Substitute \( x = 2 \), \( y = 49 \) and \( m=-1 \) into the equation: \( 49=-1\times2 + b \). Simplify the right - hand side: \( 49=-2 + b \). Add 2 to both sides to solve for \( b \): \( b=49 + 2=51 \).

Answer:

\( y=-1x + 51 \) (or \( y=-x + 51 \))