How do you graph these types of problems.
Graph each of the following inequalities.
4x + y (grater than or equal to) 4
Get y by itself on one side and then graph and shade the region depending on the sign (< or >) and make the line dotted if it is not equal to.
"Anonymous" is correct.
The solid line above which the graph should be shaded is
y = -4x + 4
It goes through y= 4 on the y axis and has a slope of -4.
? I MAY SOUND DUMB BUT I DON'T GET IT.
i still don't get it
4x + y >= 4
You have to draw a figure that shows which coordinates (x,y) satisfy the inequality and which don't. It's easiest to consider the border line. At the border
4x + y = 4 --->
y = 4 - 4x
You draw this line forst. The line itself belongs to the region and all points that are above this line, as you easily see from the inequality. The points below the line don't satisfy the inequality.
do you mean that i only have to have one line on the graph which the points go through,.(0,4) and (1,0) AM i correct or not.
Yes. There is only the one line officially on the graph. It will be a solid line because the inequality says greater than or equal to. (It would be dotted if it just said greater than.)
However, you need to shade the area above the line that you graph because there are many solutions to the inequality.
Does that help?
why do you need to shade to graph an inequality
Shading is done in order to represent the solution set of the inequality on the graph. In this case, shading above the line is done to represent the region where the values of (x, y) satisfy the inequality 4x + y >= 4.
This shading shows that any point located in the shaded region of the graph will make the inequality true, while points outside of the shaded region will not satisfy the inequality. It helps to visually identify and understand the set of solutions to the inequality.
Shading is used to visually represent all the points in the coordinate plane that satisfy the inequality. In the case of the inequality 4x + y >= 4, the shaded area above the line indicates that any point in that region would make the inequality true.
By shading the correct region, you can quickly identify which points satisfy the inequality and which points do not. It helps you understand the solution set of the inequality and is an effective way to visualize the solution in the coordinate plane.