Answer:
An inequality which is not included in the graph of [tex]y < 5x+1[/tex] is: [tex]y\geq 5x+1[/tex]
Step-by-step explanation:
Given the inequality: [tex]y < 5x+1[/tex]
Since, the inequality divides the coordinate plane into 2 halves by a boundary line.
One side of the boundary line contains all solutions to the inequality and other sides of it does not contains the solution of that inequality.
For > and < : Boundary line is dashed
For ≥ and ≤ : Boundary line is solid.
Intercepts for the inequality are:
The related equation for the given inequality y =5x+1 ......[1]
x-intercepts:
Substitute y = 0 in equation [1] to solve for y:
0 = 5x+1 or
-1 = 5x
Simplify:
[tex]x = - \frac{1}{5}[/tex] = -0.2
x-intercepts is: (-0.2, 0).
y-intercepts:
Substitute x = 0 in equation [1] to solve for y:
y =5(0)+1
Simplify:
y= 1
y-intercepts is: (0 , 1).
Since, the solution is a region which is shaded for the given inequality and also the dashed line shows that the inequality does not include the line y= 5x +1 as shown below in the figure,
but the region which is not included in the graph of [tex]y < 5x+1[/tex] is: [tex]y\geq 5x+1[/tex]
