Graph the inequality 2X - 4Y < 8
Use the intercepts of graphs
I wonder how I'm supposed to graph here??
if you can help me in solving , and tell how to get the coordinates. that will be great help,
To graph the inequality 2X - 4Y < 8, we can start by finding the intercepts of the graph.
An intercept of a graph is the point where it crosses or touches one of the axes, either the x-axis or the y-axis. To find the x-intercept, we set Y=0 and solve for X. Similarly, to find the y-intercept, we set X=0 and solve for Y.
Let's find the x-intercept:
2X - 4(0) < 8
2X < 8
Divide both sides by 2:
X < 4
The x-intercept is X=4.
Now, let's find the y-intercept:
2(0) - 4Y < 8
-4Y < 8
Divide both sides by -4, considering that we are dividing by a negative number, the inequality flips:
Y > -2
The y-intercept is Y=-2.
Now that we have the x-intercept and y-intercept, we can plot them on a graph. The x-intercept is X=4, and the y-intercept is Y=-2.
Next, draw a dashed line through the x-intercept (4) and the y-intercept (-2). Since the inequality is < (less than), we use a dashed line to indicate that the points on this line are not included in the solution.
Finally, we need to determine which side of the dashed line to shade. To do this, we can choose a test point that is not on the line, such as (0, 0), and substitute it into the inequality:
2X - 4Y < 8
2(0) - 4(0) < 8
0 - 0 < 8
0 < 8
Since the test point (0, 0) satisfies the inequality, we shade the side of the line containing the origin (0, 0).
Therefore, the solution to the inequality 2X - 4Y < 8 is the shaded region below the dashed line.