3x + 4y less than or equal to -12
Graph linear inequality
Just first plot the line where 3x+4y = 12
This is the line y = -(3/4)x + 3
Since you are dealing with the graph of an inequality, you will have to indicate an area where the inequality holds. since 3x+4y has to be less than or equal to -12, that area equals the area under the line you just drew.
To graph the linear inequality 3x + 4y ≤ -12, you can follow these steps:
Step 1: Start by graphing the line 3x + 4y = -12. To do this, solve the equation for y and put it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, rearrange the equation:
3x + 4y = -12
4y = -3x - 12
y = (-3/4)x - 3
Step 2: Plot the y-intercept, which is -3. On the coordinate plane, locate the point (0, -3).
Step 3: Determine the slope. The coefficient of x in the equation, -3/4, represents the slope. For every unit increase in x, the line moves down by 3/4 units. Slope is "rise over run," meaning you move down by 3 and right by 4 units to find the next point.
Step 4: Plot additional points. Starting from the y-intercept, move down 3 units and right 4 units to find the next point (4, -6). Connect the two points with a straight line since we are dealing with a linear equation.
Step 5: Determine the shading. Since the inequality symbol is "less than or equal to," we need to determine which side of the line to shade. Choose a point not on the line, such as (0,0), and substitute its x and y coordinates into the inequality: 3(0) + 4(0) ≤ -12. Simplifying, we get 0 ≤ -12, which is false. Therefore, we shade the side opposite the region containing the point (0,0).
Step 6: Shade the region. Shade the area below the line to represent the solution to the inequality.
That's it! You've successfully graphed the linear inequality 3x + 4y ≤ -12.