Question

the table shows a linear relationship between x and y.

x	y
-4	5
0	3
4	1
12	-3

write an equation that describes the relationship shown in the table. move the correct answer to each box. not all answers will be used.
options: -4, -3, -1/4, 1/4, 3, 4

Explanation:

Step1: Find the slope

We use two points, say \((x_1,y_1)=(-8,5)\) and \((x_2,y_2)=(12,0)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 5}{12-(-8)}=\frac{-5}{20}=-\frac{1}{4}\).

Step2: Use point - slope form

Using the point \((0,3)\) (since when \(x = 0\), \(y = 3\), this is the y - intercept \(b = 3\)), the slope - intercept form of a line is \(y=mx + b\). Substituting \(m=-\frac{1}{4}\) and \(b = 3\), we get \(y=-\frac{1}{4}x+3\).

Answer:

\(y =-\frac{1}{4}x + 3\)