Question

ellen thinks that if a line has no slope, then it never touches the y - axis. which line proves that her statement is incorrect?
o x = 0
o y = 0
o x = 1
o y = 1

Explanation:

Step1: Recall slope - zero line

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

Step2: Analyze $y$-intercept

For the line $y = 1$, its slope $m = 0$ (since for any two points $(x_1,1)$ and $(x_2,1)$ on the line, $m=\frac{1 - 1}{x_2 - x_1}=0$). And it touches the $y$-axis at the point $(0,1)$. So it disproves the statement that a line with no slope never touches the $y$-axis.

Step3: Analyze other options

The line $x = 0$ is the $y$-axis itself and has an undefined slope. The line $y = 0$ is the $x$-axis with slope $m = 0$ but it touches the $y$-axis at infinitely many points. The line $x=1$ is a vertical line with an undefined slope.

Answer:

D. $y = 1$