For the equation we’ll derive, we’ll represent the value that we want to find a corresponding value for as ‘’x’’ and the interpolated value we want to find as ‘’y’’. (We’ll use these labels, because on a graph, the value we know would be plotted on the horizontal, or x-axis, and the value we’re trying to find would be plotted on the vertical, or y-axis. ) Our ‘’x’’ value will be the temperature of the gas, which for this example will be 37 °C (99 °F).

Because we’re representing the temperature of 37 °C (99 °F) with ‘’x’’, we’ll represent the temperature of 30 degrees as ‘’x1’’ and the value of 40 degrees as ‘’x2’’. {“smallUrl”:“https://www. wikihow. com/images/thumb/2/26/Interpolate-Step-2Bullet1-Version-2. jpg/v4-460px-Interpolate-Step-2Bullet1-Version-2. jpg”,“bigUrl”:"/images/thumb/2/26/Interpolate-Step-2Bullet1-Version-2. jpg/aid3863515-v4-700px-Interpolate-Step-2Bullet1-Version-2. jpg",“smallWidth”:460,“smallHeight”:368,“bigWidth”:700,“bigHeight”:560,“licensing”:"<div class="mw-parser-output">

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<br />\n</p></div>"} Because we’re representing the pressure were trying to find with ‘’y’’, we’ll represent the pressure of 3 kPa at 30 °C (86 °F) as ‘’y1’’ and the pressure of 5 kPa at 40 °C (104 °F) as ‘’y2’’. {“smallUrl”:“https://www. wikihow. com/images/thumb/b/b4/Interpolate-Step-2Bullet2-Version-2. jpg/v4-460px-Interpolate-Step-2Bullet2-Version-2. jpg”,“bigUrl”:"/images/thumb/b/b4/Interpolate-Step-2Bullet2-Version-2. jpg/aid3863515-v4-700px-Interpolate-Step-2Bullet2-Version-2. jpg",“smallWidth”:460,“smallHeight”:368,“bigWidth”:700,“bigHeight”:560,“licensing”:"<div class="mw-parser-output">

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Plugging in the values for x, x1, and x/2 in their places gives (37 – 30)/(40 -30), which reduces to 7/10 or 0. 7. {“smallUrl”:“https://www. wikihow. com/images/thumb/5/5d/Interpolate-Step-3Bullet1-Version-2. jpg/v4-460px-Interpolate-Step-3Bullet1-Version-2. jpg”,“bigUrl”:"/images/thumb/5/5d/Interpolate-Step-3Bullet1-Version-2. jpg/aid3863515-v4-700px-Interpolate-Step-3Bullet1-Version-2. jpg",“smallWidth”:460,“smallHeight”:368,“bigWidth”:700,“bigHeight”:560,“licensing”:"<div class="mw-parser-output">

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<br />\n</p></div>"} Plugging in the values for y1 and y2 at the end of the equation gives (5 – 3) or 2. {“smallUrl”:“https://www. wikihow. com/images/thumb/f/f2/Interpolate-Step-3Bullet2-Version-2. jpg/v4-460px-Interpolate-Step-3Bullet2-Version-2. jpg”,“bigUrl”:"/images/thumb/f/f2/Interpolate-Step-3Bullet2-Version-2. jpg/aid3863515-v4-700px-Interpolate-Step-3Bullet2-Version-2. jpg",“smallWidth”:460,“smallHeight”:368,“bigWidth”:700,“bigHeight”:560,“licensing”:"<div class="mw-parser-output">

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<br />\n</p></div>"} Multiplying 0. 7 by 2 gives a product of 1. 4. Adding 1. 4 to the value of y1, or 3, gives a value of 4. 4 kPa. Checking this against our original values, 4. 4 falls between 3 kPa at 30 °C (86 °F) and 5 kPa at 40 °C (104 °F), and because 37 is closer to 40 than it is to 30, the result should be closer to 5 kPa than it is to 3 kPa. {“smallUrl”:“https://www. wikihow. com/images/thumb/2/22/Interpolate-Step-3Bullet3-Version-2. jpg/v4-460px-Interpolate-Step-3Bullet3-Version-2. jpg”,“bigUrl”:"/images/thumb/2/22/Interpolate-Step-3Bullet3-Version-2. jpg/aid3863515-v4-700px-Interpolate-Step-3Bullet3-Version-2. jpg",“smallWidth”:460,“smallHeight”:368,“bigWidth”:700,“bigHeight”:560,“licensing”:"<div class="mw-parser-output">

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