My book uses the slope y-intercept method for graphing.
I am trying to graph the following:
y>3/2x-5/2
(sign > is greater then or equal to)
The way I understand it I would start on the Y axis at 0 and go down 5 and then to the right 2 for the -5/2. Then I would go up 3 and to the right 2 for the 3/2. The book shows(0,3/2) and (2,-7/2) as the coordinates. I have tried several different ways. I do not arrive at these coordinates.
No, the first step in your process is wrong.
The -5/2 IS the y-intercept and -5/2 is -2.5
So you are at (0,-2.5), now go up 3 and to the right 2, for the second point (2,0.5)
In fraction form these points should be
(0, -5/2) and (2,1/2)
Join them with a solid line, and shade in the region above the line.
Unless you typed the inequation incorrectly, the book answers you supplied are wrong.
Thank you for your response.
This is a rough graph with the exact coordinates stated in the book.
Y
-
-
.(0,3/2)
-
0 ' ' ' ' 'X
-
-
- .(2,-7/2)
-
-
My point was and my point still is that the book is wrong if these points are supposed to satisfy the "equation" part of the inequality.
The points I gave you DO satisfy the equation part of the inequality, thus they establish the boundary of the region you want.
To graph the inequality y > 3/2x - 5/2 using the slope-intercept method, you first need to convert the inequality into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the given inequality is already in slope-intercept form with m = 3/2 and b = -5/2.
To graph the inequality, you can follow these steps:
1. Start by marking the y-intercept. In this case, the y-intercept is at y = -5/2. Mark a point on the y-axis at this y-coordinate.
2. Use the slope to find another point on the line. The slope is 3/2, which means that for every 2 units you move to the right, you need to move up 3 units.
- From the y-intercept, move 2 units to the right.
- Then, move up 3 units from the starting point and mark another point.
3. Draw a dashed line connecting the two points. Since the inequality is y > 3/2x - 5/2, the line should be dashed to indicate that the points on the line are not included in the solution set.
Now, let's verify the coordinates mentioned in the book: (0, 3/2) and (2, -7/2).
To do this, you can substitute the x-values into the equation y = 3/2x - 5/2:
For x = 0:
y = 3/2(0) - 5/2 = -5/2 = -2.5
So, the point (0, -2.5) is incorrect. It seems there may be a mistake in the book.
For x = 2:
y = 3/2(2) - 5/2 = 6/2 - 5/2 = 1/2 = 0.5
So, the point (2, 0.5) is correct.
To summarize, the correct point on the line should be (2, 0.5), not (0, 3/2).