How do you differentiate y>2x+1 from y =2x+1
solutions to y=2x+1 are a set of points that lie on a line
The solutions to y > 2x+1 is all the points in the x-y plane that lie above the line. That is, all the points where y is greater than it is on the line y=2x+1.
you can find many examples of graphing inequalities online.
To differentiate between the two equations, we need to understand the difference in their meanings.
The equation y = 2x + 1 represents a straight line where the y-coordinate is always equal to 2 times the x-coordinate plus 1. This equation shows an exact equality between the left-hand side and the right-hand side.
On the other hand, y > 2x + 1 represents an inequality. It means that the y-coordinate is greater than the value obtained by substituting any x-coordinate into the equation 2x + 1.
To graphically differentiate between the two, you can plot the points that lie on the line y = 2x + 1. This line will represent the boundary separating the two regions: the area where y > 2x + 1 and the area where y is less than or equal to 2x + 1.
For example, if you choose a point not on the line (like (0,0)), you can substitute its coordinates into both equations. If the resulting inequality is true for y > 2x + 1 but false for y = 2x + 1, then you can determine that the point lies in the region y > 2x + 1.