How do you graph #3x - 2y ≥ 6#?

Question

HIX Tutor · Accepted Answer

undefined To graph the inequality 3x - 2y ≥ 6, follow these steps:
1. Rearrange the inequality to solve for y: y ≤ (3/2)x - 3.
2. Start by graphing the line y = (3/2)x - 3 by plotting the y-intercept at (0, -3) and using the slope of 3/2 to find another point.
3. Since the inequality is y ≤ (3/2)x - 3, shade the area below the line to represent the solution.
4. Make the line solid since the inequality includes "or equal to."
5. Label the graph to make it clear which area represents the solution.

Kennedy Adams · Answer

See a solution process below:

To find the inequality's boundary line, first solve for two points as an equation rather than as an inequality. For: #x = 0# #(3 * 0) - 2y = 6# #0 - 2y = 6# #-2y = #6# Color(red)(-2) / #(-2y) = 6/color(red)(-2)# #(0, -3)# or #y = -3# For: #y = 0# #3x - (2 xx 0) = 6# #3x - 0 = 6# #3x equals #6# Color(red)(3) / #(3x) = 6 / color(red)(3)# #x = 2# or #(2, 0)# Now that we have graphed the two points on the coordinate plane, we can draw a solid boundary line through the points to indicate the location of the inequality. This is because the inequality operator has an "or equal to" clause. graph{3x-2y-6)=0 [-10, 10, -5, 5]}(x^2+(y+3)^2-0.04)((x-2)^2+y^2-0.04) We can now shade the line's right side. plot{(3x-2y-6) >= 0 [-10, 10, -5, 5]}

Avery Alexander · Answer

undefined To graph the inequality 3x - 2y ≥ 6, first, rearrange it to solve for y: y ≤ (3/2)x - 3. Then, plot the line y = (3/2)x - 3. Since it's a "greater than or equal to" inequality, shade the area below the line.