Question

The table shows the relationship of how many pounds of pecans are needed to make a certain number of pies:

Pounds of Pecans
3=2 numbers of pies

6=4 numbers of pies

9=6 numbers of pies

Which graph below shows plots of equivalent ratios for this situation?

A. A graph is drawn. The horizontal axis and vertical axis values are 0 to 70 in increments of 10. The horizontal axis label is Number of Pies, and the vertical axis label is Pounds of Pecans. Points are plotted on the ordered pairs 15, 10 and 30, 20 and 45, 30.


B. A graph is drawn. The horizontal axis and vertical axis values are 0 to 70 in increments of 10. The horizontal axis label is Number of Pies, and the vertical axis label is Pounds of Pecans. Points are plotted on the ordered pairs 10, 15 and 20, 30 and 30, 45.


C. A graph is drawn. The horizontal axis and vertical axis values are 0 to 70 in increments of 10. The horizontal axis label is Number of Pies, and the vertical axis label is Pounds of Pecans. Points are plotted on the ordered pairs 15, 10 and 25, 10 and 35, 10.


D.A graph is drawn. The horizontal axis and vertical axis values are 0 to 70 in increments of 10. The horizontal axis label is Number of Pies, and the vertical axis label is Pounds of Pecans. Points are plotted on the ordered pairs 10, 30, and 20, 20 and 30, 10.

Answer 1

Let us take no. of pies to be x (will be represented in the horizontal, x-axis) and no. of pounds of pecans to be y (will be represented in the vertical y-axis).

The points will be

(x₁, y₁) = (2,3)

(x₂,y₂) = (4,6)

(x₃,y₃) = (6,9)

The slope, m = (Change in y)/(change in x)

So, here the slope, m = (6-3)/(4-2) = 3/2

We need to find the graph with the slope 3/2 from the given options.

Option A : Slope = (20-10)/(30-15) =10/15 =2/3 : NO

Option B : Slope = (30-15)/(20-10) = 15/10 =3/2 : YES

Option C : Slope = (10-10)/(25-10) =0 : NO

Option D : Slope = (20-30)/(20-10) = -10/10 =-1 :NO

So, we see that of the given options only graph of option B has the same slope as the given relationship.

Hence, option B is the answer.