Question

which equation below corresponds to the table of values? *

x	y
-1	2.5
0	2
1	1.5
2	1

○ y= 0.5x+2
○ y= -0.5x+2
○ x= (1/2)y+0.5
○ x= (-1/2)y+2

Explanation:

Step1: Recall linear equation form

The general form of a linear equation is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. The y - intercept \( b \) is the value of \( y \) when \( x = 0 \). From the table, when \( x = 0 \), \( y = 2 \), so \( b = 2 \).

Step2: Calculate 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 two points, for example, \( (0,2) \) and \( (1,1.5) \). Then \( m=\frac{1.5 - 2}{1 - 0}=\frac{- 0.5}{1}=- 0.5 \).

Step3: Form the equation

Using the slope - intercept form \( y=mx + b \), with \( m=-0.5 \) and \( b = 2 \), the equation is \( y=-0.5x + 2 \). We can also verify this equation with other points from the table. For example, when \( x=-2 \), \( y=-0.5\times(-2)+2 = 1 + 2=3 \), which matches the table. When \( x = 2 \), \( y=-0.5\times2+2=-1 + 2 = 1 \), which also matches the table.

Answer:

\( y=-0.5x + 2 \) (corresponding to the option \( y=-0.5x + 2 \))