Question

order the following graphs by increasing slope of the line being displayed:

enter the labels of the graphs (a, b, c, and d) in order of increasing slope:
slope (square) < slope (square) < slope (square) < slope (square).

Explanation:

Step1: Identify slope direction & steepness

• Graph A: Negative, steep slope
• Graph B: Positive, steep slope
• Graph C: Positive, gentle slope
• Graph D: Negative, gentle slope

Step2: Rank negative slopes first

Negative slopes are less than positive. Steeper negative slope has smaller value: $\text{Slope } A < \text{Slope } D$

Step3: Rank positive slopes next

Gentler positive slope has smaller value: $\text{Slope } C < \text{Slope } B$

Step4: Combine all rankings

Negative slopes < positive slopes, so full order: $\text{Slope } A < \text{Slope } D < \text{Slope } C < \text{Slope } B$

Answer:

Slope $\boldsymbol{A}$ < Slope $\boldsymbol{D}$ < Slope $\boldsymbol{C}$ < Slope $\boldsymbol{B}$