Which Graph represents the given inequality?
y>5x-1
the graph that shows the region above
y = 5x - 1, with the line shown as a dotted line
Why did the inequality go to therapy?
Because it couldn't handle being greater than everything all the time.
But hey, let's find the graph that represents this inequality! The correct graph should have a line that is greater than and does not include the points on the line. So, picture a line with a positive slope, starting below the point (0, -1) and going up from there. Don't forget to draw some shading above the line to represent the "greater than" part. Voila! You've got the graph that represents y > 5x - 1.
To represent the inequality y > 5x - 1 graphically, we need to create a graph of the equation y = 5x - 1 first and then shade the region above the line.
Here are the steps to create the graph:
Step 1: Draw a coordinate plane or XY-plane.
Step 2: Plot the y-intercept (0, -1) by going down 1 unit from the origin on the y-axis.
Step 3: Use the slope "5" to create more points. The slope tells us that for every 1 unit we move to the right, y increases by 5 units. So, from the y-intercept (0, -1), move 1 unit right and 5 units up to plot the point (1, 4), then move 1 unit right and 5 units up again to plot the point (2, 9).
Step 4: Connect the plotted points with a straight line as it represents the equation y = 5x - 1.
Step 5: Finally, since the inequality y > 5x - 1 states that y is greater than the line, we need to shade the region above the line. You can shade the region above the line by drawing a dashed line instead of a solid line.
Therefore, the graph that represents the given inequality y > 5x - 1 is a dashed line passing through the points (0, -1), (1, 4), and (2, 9), with the region above the line shaded.
To determine which graph represents the given inequality y > 5x - 1, we need to understand the characteristics of the inequality and how it translates to a graph.
The inequality y > 5x - 1 represents a linear inequality in two variables (x and y). To graph this inequality, we can follow the steps:
1. Start by graphing the line y = 5x - 1, which is the equation formed by replacing the inequality symbol with an equal sign. This line is known as the boundary line.
The equation y = 5x - 1 represents a straight line with a slope of 5 (the coefficient of x) and a y-intercept of -1 (the constant term).
2. Since the inequality is y > 5x - 1, the graph should represent the solution region where y is greater than the line y = 5x - 1. This means the area above the line needs to be shaded.
To confirm the correct graph, let's compare the options and choose the one that satisfies the inequality y > 5x - 1.