Solve the inequality y<-2/3x+1 by graphing
To graph the inequality y < -2/3x + 1, we can follow these steps:
Step 1: Plot the y-intercept.
The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is (0, 1). Plot this point on the graph.
Step 2: Find a second point on the line.
To find a second point, you can choose any value for x and plug it into the equation to solve for y. Let's plug x = 3:
y = -2/3(3) + 1
y = -2 + 1
y = -1
So, the point (3, -1) is on the line. Plot this point on the graph.
Step 3: Draw the line.
Use the two points plotted to draw a straight line passing through them. This line represents the equation y = -2/3x + 1.
Step 4: Shade the region below the line.
Since the inequality is y < -2/3x + 1, we need to shade the region below the line. This means that any point below the line should be included. Shade the region below the line.
The graph of the inequality y < -2/3x + 1 should look like this:
(graph as shown below)
Note: The line should be dashed since the inequality does not include the points on the line itself.