Question

1. which one of these equations has its graph as a horizontal line? (a) 2x = 6 (b) 2y + 6 = 0 (c) x + 6y = 0 (d) x - 6 = 0

Explanation:

Step1: Recall line - form rules

The equation of a horizontal line is of the form $y = k$, where $k$ is a constant.

Step2: Rearrange each option

• Option (a): Solve $2x = 6$ for $x$, we get $x=3$, which is a vertical line.
• Option (b): Solve $2y + 6 = 0$ for $y$. First, subtract 6 from both sides: $2y=-6$. Then divide by 2: $y=-3$. This is a horizontal line.
• Option (c): Solve $x + 6y = 0$ for $y$, we have $y=-\frac{1}{6}x$, which is a non - horizontal straight line with slope $-\frac{1}{6}$.
• Option (d): Solve $x - 6 = 0$ for $x$, we get $x = 6$, which is a vertical line.

Answer:

B. $2y + 6 = 0$