Question

write the linear equation that gives the rule for this tal
x | y
0 | 56
1 | 16
2 | -24
3 | -64
write your answer as an equation with y first, followed

Explanation:

Step1: Find the slope (m)

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((0, 56)\) and \((1, 16)\):
\( m=\frac{16 - 56}{1 - 0}=\frac{-40}{1}=-40 \)

Step2: Find the y-intercept (b)

The y - intercept is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 56 \), so \( b = 56 \).

Step3: Write the linear equation

The slope - intercept form of a linear equation is \( y=mx + b \). Substituting \( m=-40 \) and \( b = 56 \) into the equation:
\( y=-40x + 56 \)

Answer:

\( y=-40x + 56 \)