# Question Video: Finding the Value of the Coefficient of π₯ in a Linear Function given its Value at a Certain π₯-Value Mathematics • 8th Grade

Find the value of π given π(π₯) = ππ₯ + 13 and π(8) = β11.

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### Video Transcript

Find the value of π given π of π₯ equals ππ₯ plus 13 and π of eight is equal to negative 11.

Here is our function. π is sort of the name of the function. And π₯ is what goes in; itβs its input. Weβve also been given some information about the value of π of eight. In other words, our input is no longer π₯. Itβs eight. And when the input is eight, the output is negative 11. So, letβs see what happens when we put eight into our definition of the function here.

π of eight means each time we see the π₯, we replace or substitute it with eight. So, π of eight becomes π times eight plus 13. Letβs write that as eight π plus 13. But of course, we know that π of eight is equal to negative 11. So, this must mean that eight π plus 13 must be equal to negative 11. And so, our job, weβre trying find the value of π, is to solve this equation.

Weβll do this by performing a series of inverse operations. The first thing weβre going to do is subtract 13 from both sides of our equation. Remember, eight π plus 13 minus 13 is just eight π. And negative 11 minus 13 means we move 13 spaces further down the number line. And we get to negative 24. So, eight π is equal to negative 24.

The eight is multiplying the π. And so, the inverse operation we apply next is to divide both sides of our equation by eight. That leaves π on the left-hand side. And since 24 divided by eight is three, we know negative 24 divided by eight is negative three. And so, given π of π₯ is equal to ππ₯ plus 13 and π of eight is equal to negative 11, we find π is equal to negative three.

Now, we can check our answer by letting π of π₯ now be equal to negative three π₯ plus 13. Weβve replaced π with negative three. Weβre going to check that the value of π of eight is indeed negative 11. And so, we replace π₯ with eight. And we get negative three times eight plus 13. Thatβs negative 24 plus 13, which is negative 11 as required.