Which linear function represents the line given by the point-slope equation y – 2 = 4(x – 3)?

Question

f(x) = 6x – 1
f(x) = 8x – 6
f(x) = 4x – 14
f(x) = 4x – 10

Answer 1

To convert the point-slope equation \( y - 2 = 4(x - 3) \) into the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, you can follow these steps:

1. Start with the equation: \[ y - 2 = 4(x - 3) \]

2. Distribute \( 4 \): \[ y - 2 = 4x - 12 \]

3. Add \( 2 \) to both sides to solve for \( y \): \[ y = 4x - 12 + 2 \] \[ y = 4x - 10 \]

Thus, the linear function that represents the line is: \[ f(x) = 4x - 10 \]

So the correct answer is: f(x) = 4x - 10