Sure! The equation given is [tex]\( y = -\frac{1}{2} x + 9 \)[/tex]. This is a linear equation in slope-intercept form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
Let’s find the values of [tex]\( y \)[/tex] for different [tex]\( x \)[/tex] values by following these steps:
### Step-by-Step Solution:
1. Identify [tex]\( x \)[/tex] values to calculate [tex]\( y \)[/tex]:
- Let's choose [tex]\( x \)[/tex] values: [tex]\(-10\)[/tex], [tex]\(-5\)[/tex], [tex]\(0\)[/tex], [tex]\(5\)[/tex], and [tex]\(10\)[/tex].
2. Calculate [tex]\( y \)[/tex] for each [tex]\( x \)[/tex]:
- For [tex]\( x = -10 \)[/tex]:
[tex]\[
y = -\frac{1}{2}(-10) + 9 = 5 + 9 = 14
\][/tex]
- For [tex]\( x = -5 \)[/tex]:
[tex]\[
y = -\frac{1}{2}(-5) + 9 = 2.5 + 9 = 11.5
\][/tex]
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = -\frac{1}{2}(0) + 9 = 0 + 9 = 9
\][/tex]
- For [tex]\( x = 5 \)[/tex]:
[tex]\[
y = -\frac{1}{2}(5) + 9 = -2.5 + 9 = 6.5
\][/tex]
- For [tex]\( x = 10 \)[/tex]:
[tex]\[
y = -\frac{1}{2}(10) + 9 = -5 + 9 = 4
\][/tex]
3. Summarize results:
- When [tex]\( x = -10 \)[/tex], [tex]\( y = 14 \)[/tex]
- When [tex]\( x = -5 \)[/tex], [tex]\( y = 11.5 \)[/tex]
- When [tex]\( x = 0 \)[/tex], [tex]\( y = 9 \)[/tex]
- When [tex]\( x = 5 \)[/tex], [tex]\( y = 6.5 \)[/tex]
- When [tex]\( x = 10 \)[/tex], [tex]\( y = 4 \)[/tex]
### Conclusion:
The values of [tex]\( y \)[/tex] corresponding to the [tex]\( x \)[/tex] values [tex]\([-10, -5, 0, 5, 10]\)[/tex] are:
[tex]\[
y = [14, 11.5, 9, 6.5, 4]
\][/tex]
These are the points on the line defined by the equation [tex]\( y = -\frac{1}{2} x + 9 \)[/tex].
