Which point lies on the line with the point-slope equation [tex]y + 5 = 2(x + 8)[/tex]?

A. [tex](8, -5)[/tex]

B. [tex](-8, -5)[/tex]

C. [tex](-8, 5)[/tex]

D. [tex](8, 5)[/tex]



Answer :

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].