Question

a horizontal line has a slope of blank. a vertical line has a slope of blank. question 12 5 pts the important rule for solving inequalities, that we dont worry about with equations is..... options: if we divide or multiply by a negative, we use an open dot. if we subtract or have negatives, we use a closed dot. if we divide or multiply by a negative, we flip the symbol. if we subtract or have negatives, we flip the symbol. if we have parentheses, we need to distribute.

Explanation:

Part 1: Slopes of Horizontal and Vertical Lines

Step1: Recall slope formula

The slope \( m \) of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Slope of horizontal line

For a horizontal line, the \( y \)-coordinates of all points are the same, so \( y_2 - y_1 = 0 \). Then \( m=\frac{0}{x_2 - x_1}=0 \) (assuming \( x_2
eq x_1 \)).

Step3: Slope of vertical line

For a vertical line, the \( x \)-coordinates of all points are the same, so \( x_2 - x_1 = 0 \). Then the slope \( m=\frac{y_2 - y_1}{0} \) is undefined (since division by zero is not allowed).

• Analyze each option:
• "If we divide or multiply by a negative, we use an open dot." → Open/closed dots relate to graphing, not inequality-solving rule distinct from equations. Eliminate.
• "If we subtract or have negatives, we use a closed dot." → Closed dots are for graphing, not a solving rule. Eliminate.
• "If we divide or multiply by a negative, we flip the symbol." → When solving inequalities, multiplying/dividing both sides by a negative reverses the inequality symbol (e.g., \( -2x > 4 \Rightarrow x < -2 \)), which is not done in equations. This matches.
• "If we subtract or have negatives, we flip the symbol." → Subtracting or having negatives does not require flipping the symbol. Eliminate.
• "If we have parentheses, we need to distribute." → Distributing is done in both equations and inequalities. Eliminate.

Answer:

A HORIZONTAL line has a slope of \( \boldsymbol{0} \).
A VERTICAL line has a slope of \( \boldsymbol{\text{undefined}} \).

Question 12: Inequality Rule