(a) The point (6, 30) means that 6 round tables can be paired or arranged alongside 30 chairs.
(b) A point that represents the unit rate of this graph is (1, 5).
(c) Yes, this is a proportional relationship because the line pass through the origin (0, 0). An equation to represent the graph is y = 5x.
In Mathematics and Geometry, a proportional relationship is a type of relationship that passes through the origin (0, 0) and produces equivalent ratios as represented by the following mathematical equation:
y = kx
Where:
- y represents the y-variable or number of chairs.
- x represents the x-variable or number of round tables.
- k is the constant of proportionality or unit rate.
Part a.
Based on the graph, the point (6, 30) means that 6 round tables can be paired or arranged alongside 30 chairs.
Part b.
Next, we would determine the unit rate (k) by using various data points in the table as follows:
Unit rate, k = y/x
Unit rate, k = 5/1 = 10/2 = 15/3
Unit rate, k = (3 × 4) = 5
Part c.
Yes, this is a proportional relationship because the graph pass through the origin (0, 0) and it's represented by a straight line. An equation to represent the graph is given by;
y = kx
y = 5x.