How do you graph #y

Question

How do you graph #y <2x - 1#?

Eva Abramson · Accepted Answer

We should first find out the values for which #y=2x-1#

The values for which #y=2x-1# lie in a straight line, as follows:

graph{2x-1 [-10, 10, -5, 5]}

For the points on the line, the y-coordinate is exactly #2x-1#; for example, the points #(1, 1)#, and the points #(2, 3)# are on the line. (See the graph).

Hence, any point above the line will satisfy #y>2x-1#, and any point #y<2x-1# will be below the line.

The solution is the set of points on the graph below the line #y=2x-1#

Abigail Allen · Answer

undefined To graph $y < 2x - 1$, first, graph the line $y = 2x - 1$. This line has a slope of 2 and y-intercept of -1.

Since the inequality is $y < 2x - 1$, the line should be drawn as a dashed line (not including the points on the line) to indicate that the points on the line are not part of the solution.

Next, choose a test point not on the line. A common choice is the origin (0,0). Substitute the coordinates of the test point into the inequality. If the inequality is true, shade the side of the line that contains the test point; if it is false, shade the other side.

For $y < 2x - 1$:
$$0 < 2(0) - 1$$
$$0 < -1$$

Since this is true, shade the side of the line that contains the origin.

How do you graph #y &lt;2x - 1#?

How do you graph #y <2x - 1#?