Sure, let's go through each part step-by-step.
### 2.1 Find the [tex]$x$[/tex]-coordinate if [tex]$y=2$[/tex]
We start with the given equation of the line:
[tex]\[ y = -\frac{1}{2} x - 2 \][/tex]
We need to find the value of [tex]\( x \)[/tex] when [tex]\( y = 2 \)[/tex]. So, we substitute [tex]\( y = 2 \)[/tex] into the equation:
[tex]\[ 2 = -\frac{1}{2} x - 2 \][/tex]
Next, we solve for [tex]\( x \)[/tex]. First, isolate the term containing [tex]\( x \)[/tex] by adding 2 to both sides of the equation:
[tex]\[ 2 + 2 = -\frac{1}{2} x \][/tex]
[tex]\[ 4 = -\frac{1}{2} x \][/tex]
Now, we need to get [tex]\( x \)[/tex] by itself. To do this, we multiply both sides of the equation by the reciprocal of [tex]\(-\frac{1}{2}\)[/tex], which is [tex]\(-2\)[/tex]:
[tex]\[ 4 \times (-2) = x \][/tex]
[tex]\[ -8 = x \][/tex]
So the [tex]\( x \)[/tex]-coordinate when [tex]\( y = 2 \)[/tex] is:
[tex]\[ x = -8 \][/tex]
### 2.2 Find the [tex]$y$[/tex]-coordinate if [tex]$x=5$[/tex]
We use the same equation of the line:
[tex]\[ y = -\frac{1}{2} x - 2 \][/tex]
Now, we need to find the value of [tex]\( y \)[/tex] when [tex]\( x = 5 \)[/tex]. Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[ y = -\frac{1}{2} \cdot 5 - 2 \][/tex]
First, calculate [tex]\(-\frac{1}{2} \cdot 5 \)[/tex]:
[tex]\[ -\frac{1}{2} \cdot 5 = -\frac{5}{2} = -2.5 \][/tex]
Now, substitute [tex]\(-2.5\)[/tex] into the equation:
[tex]\[ y = -2.5 - 2 \][/tex]
[tex]\[ y = -4.5 \][/tex]
So the [tex]\( y \)[/tex]-coordinate when [tex]\( x = 5 \)[/tex] is:
[tex]\[ y = -4.5 \][/tex]
### Summary
1. The [tex]\( x \)[/tex]-coordinate when [tex]\( y = 2 \)[/tex] is [tex]\( x = -8 \)[/tex].
2. The [tex]\( y \)[/tex]-coordinate when [tex]\( x = 5 \)[/tex] is [tex]\( y = -4.5 \)[/tex].
