How do variables you model real-world situations?

A relationship between two quantities is often expressed as an equation  in two variables. For instance, the equation:

is an equation in two variables x and y. Each order pair (a, b) will be a solution of this equation if and only if makes the equation to be true. That is, the ordered pair (1, -1) is a solution because:

In this way, the graph of an equation can  help you see relationships between real-life quantities. So, a real-world situation could be the life expectancy of a child, at birth, in the United States for selected years. So, if you are a researcher of a Research Institute you need to establish a relationship between the variable year and the variable life expectancy to know the life expectancy in each year.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.