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Micah did some research on paper consumption and recycling efforts. She found that for every ton of paper that is recycled, 17 trees are saved. Complete the table. Write an equation for this situation.
not propor

y=17 x+

$6$ . Micah did some research on paper consumption and recycling efforts. She found that for every ton of paper that is recycled, $17$ trees are saved. Complete the table. Write an equation for this situation. $\newline$ not propor $\newline$ $y=17 x+$

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Write and solve direct variation equations

Full solution

Q.

6

. Micah did some research on paper consumption and recycling efforts. She found that for every ton of paper that is recycled,

17

trees are saved. Complete the table. Write an equation for this situation.

\newline

not propor

\newline

y=17 x+

Identify Relationship: Identify the relationship between the number of trees saved and the tons of paper recycled. $\newline$ The problem states that for every ton of paper recycled, $17$ trees are saved. This is a direct variation because the number of trees saved increases proportionally with the amount of paper recycled.
Determine Constant: Determine the constant of variation, $k$ . Since $17$ trees are saved for every ton of paper recycled, the constant of variation $k$ is $17$ .
Write Equation: Write the direct variation equation using the constant of variation. $\newline$ The general form of a direct variation equation is $y = kx$ . Here, $y$ represents the number of trees saved, and $x$ represents the tons of paper recycled. Substituting the constant of variation $k = 17$ , we get the equation $y = 17x$ .
Check with Information: Check the equation with the given information. $\newline$ If we substitute $x = 1$ (for $1$ ton of paper recycled) into the equation $y = 17x$ , we should get $y = 17$ , which means $17$ trees are saved. This matches the information given in the problem, confirming that the equation is correct.

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