Question

Let us consider the points with an integer y-coordinate from (−1) to 1 and with an integer x-coordinate from (-20) to 20. How many lines are there parallel to the line y=2x and passing through any of these points?

Answer 1

There are five lines parallel to y=2x passing through the given points.

Step-by-step explanation:

Given the line y=2x and the range of x and y coordinates provided, we can determine how many lines parallel to y=2x pass through any of the given points.

To find such lines, we need to identify the points (x, y) that satisfy the equation y=2x, where x ranges from -20 to 20 and y ranges from -1 to 1.

Let's examine each possible y-coordinate and find the corresponding x-coordinate that satisfies the equation.

Thus, we have:

1. x = -10, y = -20
2. x = -5, y = -10
3. x = 0, y = 0
4. x = 5, y = 10
5. x = 10, y = 20

For each of these points, we can create a line parallel to y=2x. Based on the given range of x-coordinates, we can form a total of five lines.