Let's solve the given question step by step by finding the [tex]\( y \)[/tex]-values for each [tex]\( x \)[/tex]-value using the equation [tex]\( y = -\frac{1}{2}x + 3 \)[/tex].
### Step 1: Calculate [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]
Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[
y = -\frac{1}{2}(0) + 3
\][/tex]
This simplifies to:
[tex]\[
y = 3
\][/tex]
So, the point [tex]\((0, y)\)[/tex] becomes [tex]\((0, 3)\)[/tex].
### Step 2: Calculate [tex]\( y \)[/tex] when [tex]\( x = 4 \)[/tex]
Substitute [tex]\( x = 4 \)[/tex] into the equation:
[tex]\[
y = -\frac{1}{2}(4) + 3
\][/tex]
This simplifies to:
[tex]\[
y = -2 + 3 = 1
\][/tex]
So, the point [tex]\((4, y)\)[/tex] becomes [tex]\((4, 1)\)[/tex].
### Step 3: Calculate [tex]\( y \)[/tex] when [tex]\( x = -2 \)[/tex]
Substitute [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[
y = -\frac{1}{2}(-2) + 3
\][/tex]
This simplifies to:
[tex]\[
y = 1 + 3 = 4
\][/tex]
So, the point [tex]\((-2, y)\)[/tex] becomes [tex]\((-2, 4)\)[/tex].
### Summary of Points
1. When [tex]\( x = 0 \)[/tex], [tex]\( y = 3 \)[/tex]. The point is [tex]\((0, 3)\)[/tex].
2. When [tex]\( x = 4 \)[/tex], [tex]\( y = 1 \)[/tex]. The point is [tex]\((4, 1)\)[/tex].
3. When [tex]\( x = -2 \)[/tex], [tex]\( y = 4 \)[/tex]. The point is [tex]\((-2, 4)\)[/tex].
Therefore, the values of [tex]\( y \)[/tex] corresponding to [tex]\( x \)[/tex] values of [tex]\( 0, 4, \)[/tex] and [tex]\( -2 \)[/tex] are [tex]\( 3.0, 1.0, \)[/tex] and [tex]\( 4.0 \)[/tex], respectively.
