Final answer:
To find the linear inequality with a solution set below the line through points (0,3) and (2,1), calculate the slope as -1 and use it in the slope-intercept form y = mx + b. The inequality is y < -x + 3, making the correct answer (d).
Step-by-step explanation:
The task is to find a linear inequality with a solution set that represents shading the region below the line passing through the points (0, 3) and (2, 1). To find this inequality, we must first determine the equation of the line that passes through these points.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula m = (y2 - y1) / (x2 - x1). Using the given points (0, 3) and (2, 1), the slope can be calculated as m = (1 - 3) / (2 - 0) = -2 / 2 = -1. Now we know the slope of our line is -1.
A line equation in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through (0, 3), our y-intercept is 3. Thus, the line equation is y = -1x + 3, or simply y = -x + 3.
The inequality that represents shading below this line would be y < -x + 3. Therefore, the correct option is (d) y < -x + 3. This linear inequality indicates that the solution set includes all the points below the line.
As an MCQ answer in the final answer, the correct choice is (d) y < -x + 3.