Final answer:
To graph the inequality 2x + 5y > 10, convert it to slope-intercept form (y = mx + b), plot the y-intercept, and draw a dashed line with the given slope. Shade the area above the line to satisfy the inequality.
Step-by-step explanation:
To graph the inequality 2x + 5y > 10, we need to first convert it to slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. Rearrange the inequality to isolate y: 5y > -2x + 10. Divide both sides by 5 to solve for y: y > -2/5x + 2. Now we can graph the inequality. Start by plotting the y-intercept, which is the point (0, 2). Since the inequality is y > -2/5x + 2, draw a dashed line passing through (0, 2) with a slope of -2/5. Shade the area above the line to indicate that all the points above the line satisfy the inequality.