Question Video: Writing a Linear Equation from a Table of Values | Nagwa Question Video: Writing a Linear Equation from a Table of Values | Nagwa

# Question Video: Writing a Linear Equation from a Table of Values Mathematics

Write the equation that expresses π¦ in terms of π₯ for the numbers in the table.

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### Video Transcript

Write the equation that expresses π¦ in terms of π₯ for the numbers in the table.

That first row in the table shows us a list of values for π₯. π₯ is just a letter that weβre using to represent different numbers here. The second row in the table shows us a list of values for π¦. So when π₯ is zero, π¦ equals seven. When π₯ is one, π¦ equals eight. When π₯ is two, π¦ equals nine. And when π₯ equals three, π¦ equals 10. This problem asked us to write the equation that expresses π¦ in terms of π₯. What does this mean? An equation is where we say something is worth the same as something else. And weβre using equal sign to show that itβs worth the same. Weβre asked to express π¦ in terms of π₯. Another way to say this is, what is π¦ worth? π¦ equals what? And on the right-hand side of our equation, we have to mention π₯. Letβs look at what we do to π₯ to get to each value of π¦.

Weβve said already when π₯ is worth zero, π¦ is worth seven. This is a difference of seven. We add seven to zero to get seven. What about when π₯ is worth one? Weβre told that when π₯ equals one, π¦ equals eight. Again this is a difference of seven. One plus seven equals eight. In fact the plus-seven rule works for all the numbers in the table. Two plus seven equals nine. And three plus seven equals 10. And so whatever the value of π₯, we just have to add seven to it to get the value of π¦. And so what is π¦ worth? Itβs worth π₯ plus seven. And so by looking at the pattern between the numbers in the table, we are able to write an equation that expresses π¦ in terms of π₯. In other words, we say what π¦ is worth in terms of what π₯ is worth. π¦ is seven more than π₯. And so we write our equation as π¦ equals π₯ plus seven.

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