how do i graph y<-x+4

Question

i need to know how to graph this equation

 

Answer 1

First find the line where y = -x +4.  Because the inequality in the problem is <, draw a doted or dashed line to show that the actual line will not be part of the solution.

 

http://hwmath.net/dev/alg/-xplus4.jpg

 

Next, decide which side of the line should be shaded. Should the point (0, 0) be part of the solution?

 

      test (0, 0): Is  0 < -(0) + 4  : yes, 0 < 4 so the point (0, 0) is part of the solution

      test (10,10) : is 10 < -10 + 4: no, 10 is not < -6 so the point (10,10) is not part of the solution.

 

In the graph shown - the solution is shown with a white background, the shaded region is NOT part of the solution.

Answer 2

First, graph the line y = -x + 4.  The line has a slope of -1 and a y-intercept of 4.  Graph the line using a dashed line; if the equation had been y ≤ -x+4, we'd use a solid line. The solid line means that all points on the line are part of the solution.  The dashed line means the points on the line are not part of the solution.

 

The line y = -x + 4 is the boundary between the solution side and the non-solution sides.  To figure out which side is the solution side, pick a point on one side and plug those values into the inequality.  A good point to pick is (0,0).  If the point satisfies the inequality, then that side is the solution side.  If it doesn't satisfy the inequality, the other side of the line is the solution side.  Shade in the solution side using hash marks.