Question

In the straight line graph of the linear equation Y = a + bX, slope is horizontal if :

• A. $b \neq 0$
• B. $b = 1$
• C. $b = 0$
• D. $a = b$

Hint:

A horizontal line has zero rise over run, meaning its slope is exactly $0$. A vertical line has an undefined (infinite) slope.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In the equation of a straight line $Y = a + bX$:
- $a$ is the $y$-intercept (the value of $Y$ when $X = 0$).
- $b$ is the slope of the line, representing the rate of change of $Y$ with respect to $X$.
Detailed Explanation:
Let us analyze the orientation of the line based on the value of the slope $b$:
- If $b > 0$, the line slopes upward from left to right.
- If $b < 0$, the line slopes downward from left to right.
- If $b = 0$, the equation simplifies to $Y = a$. This means that no matter what value $X$ takes, $Y$ remains constant at $a$.
- The graph of $Y = a$ is a perfectly horizontal line parallel to the $x$-axis.
Thus, the slope is horizontal if $b = 0$.

Step 2: Final Answer:
The slope is horizontal when $b = 0$, which corresponds to Option (C).