Question

the graph represents the perimeter, y, in units, for an equilateral triangle with side length of x units. the slope of the line is 3. the amount of money, y, in a cash box after x tickets are purchased for carnival games. the slope of the line is 1/4. the number of chapters read, y, after x days. the slope of the line is 5/4. graph a graph b graph c

Explanation:

Step1: Recall the slope formula

The slope \(m=\frac{\Delta y}{\Delta x}\). For a steeper line, the absolute value of the slope is larger.

Step2: Analyze Graph A

In Graph A, when \(x\) changes by a certain amount, \(y\) changes by a small amount. The slope is small.

Step3: Analyze Graph B

In Graph B, for a change in \(x\), \(y\) changes moderately.

Step4: Analyze Graph C

In Graph C, for a given change in \(x\), \(y\) changes more than in Graph B. Since the slope of the perimeter of an equilateral triangle \(y = 3x\) (slope \(m = 3\)), and visually, Graph C has a steeper slope compared to Graphs A and B.

Answer:

Graph C