write an equation that reflects this relationship using X to represent the amount of grams in fish and y to represent the number of calories
​

Answer:

[tex] y = \frac{3}{2}x [/tex]

Step-by-step explanation:

The graph shows there is a proportional relationship between amount of grams of fish (x) and number of calories (y).

A original relationship can be represented by An equation as [tex] y = kx [/tex], where, k = constant of proportionality (y/x).

The constant of proportionality using any point, let's say (200, 300), would be:

k = y/x = 300/200 = ³/2

Plug in the value of k into [tex] y = kx [/tex].

Thus, the equation that reflects the relationship would be:

[tex] y = \frac{3}{2}x [/tex]

The equation that reflects this relationship using x to represent the amount of fish in grams and y to represent the number of calories is (2y = 3x) and this can be determined by using the point-slope form of a line.

Given :

The point-slope form can be used to determine the equation that reflects this relationship using x to represent the amount of fish in grams and y to represent the number of calories.

The point-slope form is given by the equation:

[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]     ----- (1)

where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the points on the line.

Now, put the values of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the equation (1).

[tex]\dfrac{y-150}{x-100}=\dfrac{300-150}{200-100}[/tex]

[tex]2(y-150)=3(x-100)[/tex]

2y - 300 = 3x - 300

2y - 3x = 0

2y = 3x

The equation that reflects this relationship using x to represent the amount of fish in grams and y to represent the number of calories is (2y = 3x).

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