Question

use the drawing tools to form the correct answer on the graph.
mrs. robertson is preparing manipulatives for her math class. each student will receive a plastic cup with 20 two - color counters. the total number of two - color counters, c, that mrs. robertson needs varies directly as the number of students, s.
draw a graph showing the proportional relationship between c and s

Explanation:

Step1: Define direct variation equation

Since \(c\) varies directly with \(s\), and each student gets 20 counters, the equation is \(c = 20s\).

Step2: Identify key points

• When \(s=0\), \(c=20\times0=0\) (point \((0,0)\))
• When \(s=5\), \(c=20\times5=100\) (point \((5,100)\))
• When \(s=10\), \(c=20\times10=200\) (point \((10,200)\))
• When \(s=20\), \(c=20\times20=400\) (point \((20,400)\))

Step3: Plot and connect points

Plot the points \((0,0)\), \((5,100)\), \((10,200)\), \((20,400)\) on the graph, then draw a straight line through them (extending to the maximum \(c=400\) on the axis).

Answer:

A straight line passing through the origin \((0,0)\) and points such as \((5,100)\), \((10,200)\), \((20,400)\) on the provided coordinate grid, representing the equation \(c=20s\).