Write the equation that expresses 𝑦 in terms of 𝑥 for the numbers in the table.
That first row in the table shows us a list of values for 𝑥. 𝑥 is just a letter that we’re using to represent different numbers here. The second row in the table shows us a list of values for 𝑦. So when 𝑥 is zero, 𝑦 equals seven. When 𝑥 is one, 𝑦 equals eight. When 𝑥 is two, 𝑦 equals nine. And when 𝑥 equals three, 𝑦 equals 10. This problem asked us to write the equation that expresses 𝑦 in terms of 𝑥. What does this mean? An equation is where we say something is worth the same as something else. And we’re using equal sign to show that it’s worth the same. We’re asked to express 𝑦 in terms of 𝑥. Another way to say this is, what is 𝑦 worth? 𝑦 equals what? And on the right-hand side of our equation, we have to mention 𝑥. Let’s look at what we do to 𝑥 to get to each value of 𝑦.
We’ve said already when 𝑥 is worth zero, 𝑦 is worth seven. This is a difference of seven. We add seven to zero to get seven. What about when 𝑥 is worth one? We’re told that when 𝑥 equals one, 𝑦 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 𝑥, we just have to add seven to it to get the value of 𝑦. And so what is 𝑦 worth? It’s worth 𝑥 plus seven. And so by looking at the pattern between the numbers in the table, we are able to write an equation that expresses 𝑦 in terms of 𝑥. In other words, we say what 𝑦 is worth in terms of what 𝑥 is worth. 𝑦 is seven more than 𝑥. And so we write our equation as 𝑦 equals 𝑥 plus seven.