Question

1. given the equation of a line, $y - 3 = 4(x + 6)$, identify the two equivalent equations. $\square$ $y - 6 = 4(x + 3)$ $\square$ $y = 7x + 6$ $\square$ $y = 4x + 27$ $\square$ $4x - 3y = 6$ $\square$ $4x - y = -27$

Explanation:

Step1: Simplify the given equation

Start with \( y - 3 = 4(x + 6) \). Distribute the 4: \( y - 3 = 4x + 24 \). Then add 3 to both sides: \( y = 4x + 24 + 3 \), so \( y = 4x + 27 \).

Step2: Rewrite the simplified equation in standard form

Take \( y = 4x + 27 \) and subtract \( y \) and 27 from both sides: \( 4x - y = -27 \).

Step3: Check other options

• For \( y - 6 = 4(x + 3) \): Distribute 4: \( y - 6 = 4x + 12 \), so \( y = 4x + 18 \), not equivalent.
• For \( y = 7x + 6 \): Slope is 7, original slope is 4, not equivalent.
• For \( 4x - 3y = 6 \): Solve for y: \( -3y = -4x + 6 \), \( y = \frac{4}{3}x - 2 \), not equivalent.

Answer:

\( y = 4x + 27 \), \( 4x - y = -27 \)