To determine which point lies on the line defined by the equation [tex]\( y + 5 = 2(x + 8) \)[/tex], we will substitute the coordinates of each point into the equation and check if it holds true.
### Step-by-Step Solution:
Let's check each point one by one.
Option A: [tex]\( (8, -5) \)[/tex]
1. Substitute [tex]\( x = 8 \)[/tex] and [tex]\( y = -5 \)[/tex] into the equation [tex]\( y + 5 = 2(x + 8) \)[/tex].
2. Calculate the left side:
[tex]\[
y + 5 = -5 + 5 = 0
\][/tex]
3. Calculate the right side:
[tex]\[
2(x + 8) = 2(8 + 8) = 2 \times 16 = 32
\][/tex]
4. The equation becomes:
[tex]\[
0 \neq 32
\][/tex]
This point does not satisfy the equation.
Option B: [tex]\( (-8, -5) \)[/tex]
1. Substitute [tex]\( x = -8 \)[/tex] and [tex]\( y = -5 \)[/tex] into the equation [tex]\( y + 5 = 2(x + 8) \)[/tex].
2. Calculate the left side:
[tex]\[
y + 5 = -5 + 5 = 0
\][/tex]
3. Calculate the right side:
[tex]\[
2(x + 8) = 2(-8 + 8) = 2 \times 0 = 0
\][/tex]
4. The equation becomes:
[tex]\[
0 = 0
\][/tex]
This point satisfies the equation.
Option C: [tex]\( (-8, 5) \)[/tex]
1. Substitute [tex]\( x = -8 \)[/tex] and [tex]\( y = 5 \)[/tex] into the equation [tex]\( y + 5 = 2(x + 8) \)[/tex].
2. Calculate the left side:
[tex]\[
y + 5 = 5 + 5 = 10
\][/tex]
3. Calculate the right side:
[tex]\[
2(x + 8) = 2(-8 + 8) = 2 \times 0 = 0
\][/tex]
4. The equation becomes:
[tex]\[
10 \neq 0
\][/tex]
This point does not satisfy the equation.
Option D: [tex]\( (8, 5) \)[/tex]
1. Substitute [tex]\( x = 8 \)[/tex] and [tex]\( y = 5 \)[/tex] into the equation [tex]\( y + 5 = 2(x + 8) \)[/tex].
2. Calculate the left side:
[tex]\[
y + 5 = 5 + 5 = 10
\][/tex]
3. Calculate the right side:
[tex]\[
2(x + 8) = 2(8 + 8) = 2 \times 16 = 32
\][/tex]
4. The equation becomes:
[tex]\[
10 \neq 32
\][/tex]
This point does not satisfy the equation.
### Conclusion:
The point which lies on the line given by the equation [tex]\( y + 5 = 2(x + 8) \)[/tex] is [tex]\( \boxed{(-8, -5)} \)[/tex].
