Write an inequality that describes the region of the coordinate plane not included in the graph of
y<5x+1
y >= 5x+1
To find the region of the coordinate plane not included in the graph of y < 5x+1, we can start by writing the equation in slope-intercept form:
y < 5x + 1
To find the line that represents this equation, we can first find two points on the line by setting x = 0 and x = 1:
When x = 0:
y = 5(0) + 1
y = 1
When x = 1:
y = 5(1) + 1
y = 6
So, we have two points on the line: (0, 1) and (1, 6).
Now, let's draw the line and determine which region is not included in the graph. Since the inequality is y < 5x + 1, the line itself is not part of the region.
To represent the region not included in the graph, we can use the inequality y ≥ 5x + 1. In other words, the inequality that describes the region not included in the graph is:
y ≥ 5x + 1
To write an inequality that describes the region of the coordinate plane not included in the graph of y < 5x + 1, we need to find the complementary region by reversing the inequality sign and taking the negation. Here's how you can do it step by step:
Step 1: Start with the given inequality: y < 5x + 1.
Step 2: Reverse the inequality sign: y ≥ 5x + 1.
Step 3: Take the negation of the inequality: y ≥ -(5x + 1).
The resulting inequality, y ≥ -(5x + 1), describes the region of the coordinate plane not included in the graph of y < 5x + 1.