Graph he inequality on a plane
4y - 5x> 20
I am confused, can you please help?
4y - 5x> 20
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first look at the equality
4 y =5 x + 20
or
y = (5/4) x + 5
straight line
hits y axis at(0,5)
hits x axis at (-4,0)
above that line, for example at (0,6) you can see that 4y-5 is greater than 20 (24 in fact) so we want everything above that line
5x-4y=-18
Sure! I can help you with that. To graph the inequality 4y - 5x > 20, we can follow these steps:
Step 1: First, let's rearrange the inequality in the form of y = mx + b, where m is the slope and b is the y-intercept. This will make it easier to identify the line we need to graph.
4y - 5x > 20
Divide both sides by 4:
y - (5/4)x > 5
Subtract (5/4)x from both sides:
y > (5/4)x + 5
Step 2: Now, let's graph the line y = (5/4)x + 5.
Identify the y-intercept: The y-intercept is the value where the line crosses the y-axis. In this case, the y-intercept is 5. So, plot the point (0, 5).
Find another point on the line: To find another point, we can use the slope. The slope of the line is 5/4, which means for every increase of 4 in the x-coordinate, the y-coordinate increases by 5. Starting from the y-intercept (0, 5), move 4 units to the right (increase in x by 4) and 5 units up (increase in y by 5). Plot this point as well.
Draw a line through the two points: Now that you have two points, connect them with a straight line. This line represents the equation y = (5/4)x + 5.
Step 3: We have the line, but we also need to determine which side of the line satisfies the inequality 4y - 5x > 20.
Since the inequality is greater than (>) 20, we need to choose a test point that is not on the line. Let's use the origin (0, 0) as our test point.
Substitute the x and y coordinates of the test point into the inequality:
4(0) - 5(0) > 20
Simplify:
0 > 20
Since 0 is not greater than 20, the test point is not a solution. Thus, the side of the line not containing the test point satisfies the inequality.
Step 4: Shade the half-plane that satisfies the inequality. To do this, shade the area either above or below the line, depending on which side satisfied the inequality.
In this case, since y > (5/4)x + 5, shade the region above the line.
That's it! You have successfully graphed the inequality 4y - 5x > 20 on a plane.