To graph the linear inequality 5x - y > -3, follow these steps:
Step 1: Rearrange the inequality to y < 5x + 3
This will help to isolate 'y' and makes the inequality easier to graph.
Step 2: Identify the slope and y-intercept
From the inequality y < 5x + 3, we understood that the slope of the line is 5, and the y-intercept is 3.
Step 3: Plot the y-intercept
Start by placing a point at 3 on the y-axis.
Step 4: Use the slope to find another point
The slope of the line is 5, which can be understood as "rise/run", or how much we go up and to the right on the graph from our y-intercept. Move 5 units up and 1 unit to the right from the y-intercept to plot your next point.
Step 5: Draw a line through the points
The line should pass through the two points. Draw an arrow at each end of the line to signify that the line continues indefinitely in both directions.
Step 6: Shade the region
Since the inequality is "less than" (rather than "less than or equals to"), you should draw a dashed line. If it was "less than or equals to", you would draw a solid line. The line y = 5x + 3 is the boundary line of the shaded area.
The inequality y < 5x + 3 represents all the points below the line y = 5x + 3. So, the region to be shaded is beneath the line. Use dash lines to mark the shaded region starting from the line and moving downward, covering the area below the line.
Following these steps will give you the graph of the linear inequality 5x - y > -3.