Question

write the linear equation that gives the rule for this table.

x | y
2 | 53
3 | 49
4 | 45
5 | 41

write your answer as an equation with y first, followed by an equals sign.

submit

Explanation:

Step1: Find the slope (m)

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take the first two points \((2, 53)\) and \((3, 49)\).
\( m=\frac{49 - 53}{3 - 2}=\frac{-4}{1}=-4 \)

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \((2, 53)\) and \( m=-4 \).
Substitute into the formula: \( y - 53=-4(x - 2) \)
Expand the right - hand side: \( y - 53=-4x+8 \)
Add 53 to both sides: \( y=-4x + 8+53 \)
Simplify: \( y=-4x+61 \)

We can check with other points. For \( x = 4 \), \( y=-4\times4 + 61=-16 + 61 = 45 \), which matches the table. For \( x = 5 \), \( y=-4\times5+61=-20 + 61 = 41 \), which also matches.

Answer:

\( y=-4x + 61 \)