Question

schoology: inequalities practice test fill in the blank the inequality $y < \frac{1}{3}x - 6$ should be a \\(\boldsymbol{\downarrow}\\) line when graphed because it is a \\(\boldsymbol{\downarrow}\\) symbo. (dropdown options: solid, dotted)

Explanation:

Step1: Recall inequality line rules

For linear inequalities, if the inequality is \( y < mx + b \) or \( y > mx + b \) (strict inequality, no "or equal to"), the boundary line is dashed (dotted) because the points on the line are not included in the solution set. If the inequality is \( y \leq mx + b \) or \( y \geq mx + b \), the boundary line is solid as the line's points are included.

Step2: Analyze the given inequality

The given inequality is \( y < \frac{1}{3}x - 6 \). The inequality symbol is \( < \), which is a strict inequality (does not include equality). So, the boundary line should be dotted, and the symbol is a strict (or non - inclusive) inequality symbol.

Answer:

First blank: dotted; Second blank: strict (or non - inclusive)