y>6-2x
The inequality you've provided is \( y > 6 - 2x \). This represents a region on a coordinate plane.
To understand this inequality better, you can follow these steps:
Convert the inequality to an equation: First, consider the equation \( y = 6 - 2x \). This is the boundary line for the inequality.
Find the intercepts:
- y-intercept: Set \( x = 0 \): \[ y = 6 - 2(0) = 6 \quad \text{(point is (0, 6))} \]
- x-intercept: Set \( y = 0 \): \[ 0 = 6 - 2x \implies 2x = 6 \implies x = 3 \quad \text{(point is (3, 0))} \]
Graph the boundary line: Plot the points (0, 6) and (3, 0) and draw a dashed line through these points. The line is dashed because the inequality is "greater than" (not "greater than or equal to").
Shade the region: Since \( y > 6 - 2x \) indicates that \( y \) should be greater than the values on the line, shade the region above the line.
Test a point: To confirm which side to shade, you can test a point that is not on the line. A common choice is (0, 0): \[ 0 > 6 - 2(0) \implies 0 > 6 \quad \text{(False)} \] Since the point (0, 0) does not satisfy the inequality, it is not included in the solution region. Thus, we shade above the line \( y = 6 - 2x \).
In summary, the solution to the inequality \( y > 6 - 2x \) consists of all the points that lie above the dashed line on the graph of \( y = 6 - 2x \).
