Question

A line AB passes through the points $(4,7)$ and $(7,7)$. Which of the following is true for this scenario?

• A. AB is parallel to $x$-axis.
• B. AB is parallel to $y$-axis.
• C. Slope of AB is 0.
• D. Slope of AB is 1.

Answer 1

Answer: (A), (C)

Slope of AB is 0.

We know that, slope of the line segment whose end point coordinates are $(x_1,y_1)$ and $(x_2,y_2)$ is given by
$\frac{y_2-y_1}{x_2-x_1}$

Here, $(x_1,y_1)\equiv (4,7)$ and $(x_2,y_2)\equiv (7,7)$
$\therefore$ Slope of line segment $AB=\frac{7-7}{7-4}$
$=\frac{0}{3}=0$
Hence, the slope of the line $AB$ is $0.$
Slope of $x-$ axis is $0.$
Hence, Line AB is parallel to $x-$ axis.

Option (a), (c) are correct.