Question: (a) Select the correct choice below and, if necessary, fill in the answer box to complete your…

(a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

The slope of the line through the pair of points (2, 7) and (-3, 7), if possible, and (b) based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.

A. The slope of the line is

(Type an integer or a simplified fraction.)

B. The slope is undefined.

(b) The line through the points

• rises from left to right
• falls from left to right
• is horizontal
• is vertical

Solution

The problem is asking to find the slope of the line through the pair of points \((2, 7)\) and \((-8, 7)\) and determine whether it is horizontal or vertical. To find the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\), use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points \((2, 7)\) and \((-8, 7)\) into the formula: \[ m = \frac{7 - 7}{-8 - 2} \] \[ m = \frac{0}{-10} \] \[ m = 0 \] Since the slope \(m = 0\), the line is horizontal.