Question

Explain how the graph of y = 0.5x (the solid line on the graph) differs from the graph of y = x (the dashed line)

Answer 1

Hello there. To solve this question, we'll have to see how to identify the difference between the two lines y = 0.5x (solid line) and y = x (the dashed line)

First, usually the solid line represents itself, all the values of y such that y = 0.5x.

In this case, for every value you take for x in the real line, you divide it by two and this will be its image, the line covers all the points satisfying this relation.

The dashed line usually represents inequalities, in this case, y is not equal to x.

When you have y > x, you have a dashed line and a shadowed region covering all the plane above the line.

When you have y < x, you have a dashed line and a shadowed region covering all the plane under the line.

When y is not equal to x, you only have a dashed line.

Therefore, the dashed line represents all the points in the plane such that y is equal to x, but excluding them in some sense.