# Video: Filling the Missing Values in a Table Using a Given Linear Relation

By using the linear relation π + 2π = β8, fill in the missing values in the table.

02:04

### Video Transcript

By using the linear relation π plus two π equals negative eight, fill in the missing values in the table.

So we have π values of two and negative eight and one π value of negative three. So when π equals two, we donβt know what π is equal to. When we donβt know πβs value, we know that π is equal to negative three. And when π is equal to negative eight, we donβt know what πβs value is. So to find these missing values, we want to use the linear relation π plus two π equals negative eight.

So letβs begin by solving for π when we know that π is equal to two. So we will replace π with two and then solve for π. And in order to solve for π, we need to subtract two from both sides of the equation. So we have that two π is equal to negative 10 because negative eight minus two is negative 10. Now we must divide both sides of the equation by two. And now weβve completely isolated π.

π is equal to negative five because negative 10 divided by two is negative five. So when π is two, π is equal to negative five. And weβve plugged that in into our table. Now letβs solve for π when π equals negative three. So we replace π with negative three and we solve for π. So first, two times negative three is equal to negative six. Now we need to add six to both sides of the equation. And we find that π is equal to negative two.

So when π was negative three, π was equal to negative two. Now lastly, when we know that π is equal to negative eight, we need to find what π is equal to. So we replace π with negative eight and solve for π. So the first thing that we need to do is to add eight to both sides of the equation. And we have that two π is equal to zero because negative eight plus eight is zero. In isolating π, we divided by two on both sides of the equation and got that π is equal to zero.

So when π equals negative eight, π equals zero. So our missing values were π equals negative five, π equals negative two, and π equals zero.