Look at the graphs below.

Question

Graph K Graph P Graph F
A straight line passing through origin and point (1,3) in X-Y coordinate graph.
A straight line passing through origin and point (2,1) in X-Y coordinate graph.
A straight line passing through origin and point (2,2) in X-Y coordinate graph.
Identify the unit rate in each graph. Then, order the graphs by unit rate, from least to greatest.

Answer 1

To identify the unit rates in each graph, we first need to determine the slope of each line, as the slope represents the rate of change in the context given (X-Y coordinate graph).

1. Graph K: The line passes through the points (0,0) and (1,3).

   • Slope (unit rate) = (y2 - y1) / (x2 - x1) = (3 - 0) / (1 - 0) = 3/1 = 3.

2. Graph P: The line passes through the points (0,0) and (2,1).

   • Slope (unit rate) = (1 - 0) / (2 - 0) = 1/2.

3. Graph F: The line passes through the points (0,0) and (2,2).

   • Slope (unit rate) = (2 - 0) / (2 - 0) = 2/2 = 1.

Now that we have determined the unit rates for each graph:

• Graph K: 3
• Graph P: 1/2
• Graph F: 1

Ordering by unit rate from least to greatest:

1. Graph P: 1/2
2. Graph F: 1
3. Graph K: 3

Thus, the order from least to greatest unit rate is: Graph P, Graph F, Graph K.