Graphing with ratios :
We use ratio to compare two quantities. In case, we want to know the relationship between two quantities, we will graph the two quantities using equivalent ratios between between them.
Look at the table and answer the questions given below.
Question 1 :
Write the information in the table as ordered pairs. Use the amounts of ammonia as the x-coordinates and the amounts of distilled water as the y-coordinates.
First, let us complete the table given above.
From the first column, ratio between ammonia and distilled water is
For the first blank :
(2 ÷ 2) / (100 ÷ 2) = 1 / 50
(1 x 3) / (50 x 3) = 3 / 150
For the second blank :
(2 ÷ 2) / (100 ÷ 2) = 1 / 50
(1 ÷ 2) / (50 ÷ 2) = 0.5 / 25
(0.5 x 7) / (25 x 7) = 3.5 / 175
For the third blank :
(2 x 2) / (100 x 2) = 4 / 200
Let us write the ordered pairs in the form (x, y), where "x" represents ammonia and "y" represents distilled water.
The ordered pairs from the above table are
(2, 100), (3, 150), (3.5, 175), (4, 200), (5, 250)
Graph the ordered pairs.
Question 2 :
What do you come to know from the graph ?
From the above graph, it is clear that when the amount ammonia gets increased, the amount of distilled water also gets increased at the same rate.
Question 3 :
For each ordered pair that you graphed, write the ratio of the y-coordinate to the x-coordinate.
100/2, 150/3, 175/3.75, 200/4, 250/5
Question 4 :
The ratio of distilled water to ammonia is
How are the ratios in question no.3 related to this ratio ?
The above ratio is given between distilled water to ammonia.
Let us find the above ratio.
Already we know the ratio between distilled water to ammonia.
In the given ratio, the second quantity is 1. To make the second quantity 100/2 as 1, divide both the quantities by 2.
Then, we have
(100 ÷ 2) / (2 ÷ 2)
The above ratio is between distilled water and ammonia. In questions no.3 also, all the ratios are between distilled water and ammonia.
Hence, all the ratios in question no.3 are equivalent to the ratio 50/1.
Question 5 :
The point (2.5, 125) is on the graph below, but not in the table.
Find the ratio of the y-coordinate to the x-coordinate.
How is this ratio related to the ratios in question no.3 and 4 ?
The ratio of the y-coordinate to the x-coordinate is
125 / 2.5 = (125 x 10) / (2.5 x 10)
125 / 2.5 = 1250 / 25
125 / 2.5 = (1250 ÷ 25) / (25 ÷ 25)
125 / 2.5 = 50 / 1
This ratio 50/1 is between distilled water and ammonia.
In questions no.3 and 4 also, all the ratios are between distilled water and ammonia.
Hence, all the ratios in question no.3 and 4 are equivalent to the ratio 50/1.
Question 6 :
What do you think is true for every point on the graph ?
From the points on the graph, it is true that there is 25 ml of distilled water for every 0.5 ml of ammonia.
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