Question : What is the constant of proportionality in the equation? ----------------------------------------------------------------------------------------------------------------------------Choices: y = 5 x A) 0 B) 1 C) 4 D) 5

The ratio of the slopevalues for the given and image triangles are 5/3 and 2.5 respectively.

How to determine the ratio of the slopes from the graph

Using the information on the graph given ;

For the given triangle ;

• (2, 3) ; (0, -2)

Rise = change in y

• Rise = (-2 - 3) = -5

Run = changein x

• Run = 0 - 3 = -3

The ratio;

• -5/-3 = 5/3

For the image triangle ;

• (4, 8) ; (0, -2)

Rise = change in y

• Rise = (-2 - 8) = -10

Run = change in x

• Run = 0 - 4 = -4

The ratio ;

• -10/-4 = 2.5

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Answer:

1) 5/2 or 2.5

2) 5/2 or 2.5

Step-by-step explanation:

1) 5/2 = 2.5

2) 10/4 = 5/2 = 2.5

Because the hypotenuse of both are the segments of the same line and straight lines have the same gradient for all segments

Final answer:

Isaiah would need to place 10 units of 100 gram weights on the balance scale to counterbalance the kilogram. This is because a kilogram equates to 1000 grams and each weight is 100 grams.

Explanation:

To determine how many 100 gram weights are needed to balance a scale with a kilogram on the other side, we first need to understand that a kilogram (kg) is equivalent to 1000 grams (g). This is based on the metric system, where the prefix 'kilo-' signifies a factor of 1000.

Therefore, if Isaiah has a kilogram on one side of the scale, he has a mass of 1000 grams to balance. Given that the weights he is using are each 100 grams, he would need to use 10 of these weights to balance the mass on the scale. This because 100 (grams per weight) times 10 (weights) equals 1000 grams which is equal to the kilogram placed on the other side.

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