Question

what is the slope of the line $y = 4$?

a) 0

b) undefined

c) $-2$

d) $-10$

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Analyze the equation $y = 4$

We can rewrite the equation $y = 4$ as $y=0x + 4$. By comparing this with the slope - intercept form $y=mx + b$, we can see that the coefficient of $x$ (which is the slope $m$) is $0$. A line with a slope of $0$ is a horizontal line. For a horizontal line, the change in $y$ ($\Delta y$) between any two points is $0$, and the slope $m=\frac{\Delta y}{\Delta x}$, and since $\Delta y = 0$, the slope is $0$. A line with an undefined slope is a vertical line (where $\Delta x=0$).

Answer:

A) 0