Final answer:
To graph the inequality 5x + 2y ≥ -8, you graph the boundary line y = -5/2x - 4 with a y-intercept at -4 and a slope of -5/2, then shade the region above it. The line is solid to show that points on the line are included in the solution.
Step-by-step explanation:
To graph the inequality 5x + 2y ≥ -8, first treat it as if you're graphing the equation 5x + 2y = -8. This will give you the boundary line of the inequality. When graphing this equation, you can identify the y-intercept by setting x to zero. In this case, when x = 0, you get 2y = -8, leading to y = -4. This is the point where the line will intersect with the y-axis.
Next, to find the slope of the line, rearrange the equation into slope-intercept form (y = mx + b). In this case, 2y = -5x - 8 becomes y = -5/2x - 4. Here, -5/2 is the slope, and according to the reference, a negative slope means the line slopes downward to the right.
After plotting the y-intercept, use the slope to find another point. From the intercept (-4), move 5 units down (because the slope is -5) and 2 units to the right (because the slope is over 2). Plot this second point and draw the line through both points.
Since the original inequality is ≥ (greater than or equal to), the line will be solid, and you will shade above the line to represent all the points that satisfy the inequality 5x + 2y ≥ -8.
Labeling and Scaling
For completeness, make sure to label your graph with axis labels and to scale both axes appropriately so the points are clearly visible.