Y<2X+4
The way I unerstand from the book to graph this equation. I would start at
the Y intersect and go up to 1. The go up 2 for the slope. Then across 4 on the X axis. The book shows the graph with the coordinates of (1,6) and (0,4). When I do it the way the book explains I do not arrive at these coordinates. Y
-7
-6* (1,6)
-5
(0,4)*-4
-3
-2
-1
X' ' ' ' ' 0 1'2 3'4 5 '
Sorry about my poor looking graph.
To graph inequations (they have < or > or ≥ or ≤ in them), consider the corresponding "equation" which will become the boundary of the region you are graphing
So we would be dealing with
y = 2x + 4
put in x=1 ----> y = 2(1)+4 = 6
put in x=0 ----> y = 2(0)+4 = 4
that is how they got the two points (1,6) and (0,4)
Plot these two points, draw a dotted line, and shade in the region below that line.
for y > .... shade in above the dotted line
for y ≥ ....draw a solid line and shade in the region above
for y < .... shade in the region below, like your problem
for y ≤ .... draw a solid line, then shade in below
No problem, I can help you understand how to graph this equation correctly.
The equation you have given is Y < 2X + 4. In order to graph this inequality, we need to plot the points that satisfy this inequality.
To start, let's first graph the line Y = 2X + 4. This line has a slope of 2 and a y-intercept of 4. You can plot the y-intercept point by starting at (0, 4). From there, you can use the slope to find other points on the line. For example, from the y-intercept, you can go up 2 units and move 1 unit to the right to find another point, and so on.
However, since the inequality is Y < 2X + 4, we need to shade the region below the line, not including the line itself. This means that any point below the line should satisfy the inequality.
Looking at your graph, it seems you have correctly plotted the y-intercept point at (0, 4), but you might have made an error while finding other points. Let's double-check that by finding a few more points on the line using the same method.
Starting from the y-intercept (0, 4), if we go up 2 units and move 1 unit to the right, we get the point (1, 6). Similarly, if we go up 2 units again and move 1 unit to the right, we get the point (2, 8).
Now, to shade the region below the line, you can use a dashed line to represent the original equation Y = 2X + 4, and then shade everything below that line.
I hope this helps clarify how to graph the given inequality. Let me know if you have any further questions!