Four students were discussing how to find the unit rate for a proportional relationship. Which method is valid?
V
"Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the
"Look at the graph of the relationship. Count the number of units up and the number of units to the right onen
arrive at the next point on the graph. Write these two numbers as a fraction."
"Look at the graph of the relationship. Find the x-value of the point that corresponds to y = 2. That value is the
"Look at the graph of the relationship. Find two points which have y-values that are one unit apart. The unit ra
difference in the corresponding x-values."
0 M2

  Look at the graph of the relationship. Find the y-value of the point that corresponds to x = 1. That value is the unit rate.

Step-by-step explanation:

The unit rate is the change in y for a 1-unit change in x. Since the graph of a proportion will go through the origin, it is appropriate to look at the y-value for x = 1 (one unit from the origin).

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The ratio of units up to units to the right is also the unit rate when the fraction is reduced to lowest terms. It is a "unit" rate when the denominator of the fraction is 1 unit.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47