Question

The ordered pair (3, 1) is a solution to the linear inequality. (True or False)

Here's a description of the graph:

Coordinate Plane: It's a standard Cartesian coordinate plane with an x-axis and a y-axis.
Line: A dashed red line is graphed on the plane. This indicates that the line itself is not included in the solution set of the inequality.
Shading: The area to the left of the dashed line is shaded in red. This shaded region represents all the (x, y) coordinates that satisfy the inequality.
Slope and Intercept: The line appears to pass through the points (0, -1) and (1, 1), suggesting a slope of 2. It appears to intersect the y-axis at -1. So the equation of the boundary line is y = 2x - 1. Since the region above the line is shaded, the inequality is y > 2x - 1.

Answer 1

To determine whether the ordered pair (3, 1) is a solution to the inequality \( y > 2x - 1 \), we can substitute \( x = 3 \) and \( y = 1 \) into the inequality.

1. Substitute \( x = 3 \) into the equation of the line:
\[
y = 2(3) - 1 = 6 - 1 = 5
\]

2. Now we compare the value of \( y \) we found (which is 5) with the actual \( y \) value of the ordered pair, which is 1:
\[
1 > 5
\]

This statement is false. Since the left side (1) is not greater than the right side (5), the ordered pair (3, 1) does not satisfy the inequality \( y > 2x - 1 \).

Thus, the answer is **False**. The ordered pair (3, 1) is not a solution to the linear inequality.