Question

the table below.

x	y
-4	28
0	8
4	-12
8	-32

which equation represents the relationship in the table?
a. $y = -5x + 8$
b. $y = \frac{3}{8}x + 8$
c. $y = 5x - 8$
d. $y = \frac{1}{8}x - 8$

Explanation:

Step1: Identify the slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take two points from the table, e.g., \((-4, 28)\) and \((0, 8)\).
\( m=\frac{8 - 28}{0 - (-4)}=\frac{-20}{4}=- 5 \).

Step2: Identify the y - intercept

The y - intercept \( b \) is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 8 \), so \( b = 8 \).

Step3: Write the equation of the line

The equation of a line in slope - intercept form is \( y=mx + b \), where \( m=-5 \) and \( b = 8 \). So the equation is \( y=-5x + 8 \).

Answer:

A. \( y=-5x + 8 \)