Question

1. (3 pts) a line, y = mx + b, passes through the point (1, 6) and is parallel to y = 4x + 6. what is the value of b?

Explanation:

Step1: Determine the slope (m)

Parallel lines have equal slopes. The line \( y = 4x + 6 \) has a slope \( m = 4 \), so the line \( y = mx + b \) also has \( m = 4 \).

Step2: Substitute the point and slope into the equation

We know the line \( y = 4x + b \) passes through \( (1, 6) \). Substitute \( x = 1 \), \( y = 6 \), and \( m = 4 \) into \( y = mx + b \):
\( 6 = 4(1) + b \)

Step3: Solve for b

Simplify the equation:
\( 6 = 4 + b \)
Subtract 4 from both sides:
\( b = 6 - 4 = 2 \)

Answer:

\( b = 2 \)