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Malachi took cans to the recycling plant and put them into the can-crusher one at a time. After he had already crushed some of the cans, he started recording the number of cans he crushed per minute. This table shows how many cans Malachi put in the can-crusher at different times. Time (min) 3 5 7 9 Number of cans crushed 49 65 81 97 What is the equation that represents Malachi’s situation, where x represents the time and y represents the number of can crushed? Enter your answer in the boxes yâ’65= (xâ’ ).

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akposevictor

The equation that represents the situation, in point-slope form, is:  [tex]\mathbf{y - 65 = 8(x - 5)}[/tex]

Recall:

  • If we know the slope and a point (a pair of values), a linear equation can be written in the point-slope form as: [tex]y - y_1 = m(x - x_1)[/tex].
  • In  [tex]y - y_1 = m(x - x_1)[/tex], m = slope; [tex](x_1, y_1)[/tex] = a point or pair of values on a table.
  • Using two points or pairs of values, [tex]slope = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Thus, we are given the table as shown below (see attachment).

The slope, using (3, 49) and (5, 65) is calculated below:

[tex]slope = \frac{65 - 49}{5 - 3} = \frac{16}{2} \\\\\mathbf{slope (m) = 8}[/tex]

To write the equation in point-slope form, substitute [tex](x_1, y_1)[/tex] = (5, 65) and m = 8 into [tex]y - y_1 = m(x - x_1)[/tex].

  • Thus:

[tex]\mathbf{y - 65 = 8(x - 5)}[/tex]

Learn more about linear equation in point-slope form here:

https://brainly.com/question/19782277

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