IDNLearn.com is designed to help you find reliable answers quickly and easily. Ask anything and get well-informed, reliable answers from our knowledgeable community members.
Sagot :
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].
### 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].
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.