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Which of the following points lies on th...

Which of the following points lies on the line `y = 2x + 3` ?

A

(2, 8)

B

(3, 9)

C

(4, 12)

D

(5, 15)

Text Solution

AI Generated Solution

The correct Answer is:
To determine which of the given points lies on the line defined by the equation \( y = 2x + 3 \), we will check each point by substituting its coordinates into the equation. If the left-hand side equals the right-hand side, then the point lies on the line. Let's denote the points as follows: 1. Point A: (4, 8) 2. Point B: (3, 9) 3. Point C: (4, 12) 4. Point D: (5, 15) ### Step 1: Check Point A (4, 8) - Substitute \( x = 4 \) into the equation: \[ y = 2(4) + 3 = 8 + 3 = 11 \] - Check if \( y = 11 \) equals 8: \[ 11 \neq 8 \quad \text{(Point A does not lie on the line)} \] ### Step 2: Check Point B (3, 9) - Substitute \( x = 3 \) into the equation: \[ y = 2(3) + 3 = 6 + 3 = 9 \] - Check if \( y = 9 \) equals 9: \[ 9 = 9 \quad \text{(Point B lies on the line)} \] ### Step 3: Check Point C (4, 12) - Substitute \( x = 4 \) into the equation: \[ y = 2(4) + 3 = 8 + 3 = 11 \] - Check if \( y = 11 \) equals 12: \[ 11 \neq 12 \quad \text{(Point C does not lie on the line)} \] ### Step 4: Check Point D (5, 15) - Substitute \( x = 5 \) into the equation: \[ y = 2(5) + 3 = 10 + 3 = 13 \] - Check if \( y = 13 \) equals 15: \[ 13 \neq 15 \quad \text{(Point D does not lie on the line)} \] ### Conclusion The only point that satisfies the equation \( y = 2x + 3 \) is Point B (3, 9). Therefore, the answer is: **Point B (3, 9) lies on the line \( y = 2x + 3 \).**
To determine which of the given points lies on the line defined by the equation \( y = 2x + 3 \), we will check each point by substituting its coordinates into the equation. If the left-hand side equals the right-hand side, then the point lies on the line. Let's denote the points as follows: 1. Point A: (4, 8) 2. Point B: (3, 9) 3. Point C: (4, 12) 4. Point D: (5, 15) ...
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