Translate the following phrase into an inequality, then graph it
The sum of 3 times x and 1 times y is greater than or equal to 0
3x + y > 0
Cannot graph here.
To translate the phrase "The sum of 3 times x and 1 times y is greater than or equal to 0" into an inequality, we can use the following equation:
3x + y ≥ 0
To graph this inequality, we first need to convert it into slope-intercept form, which is y ≥ -3x. This equation represents a line with a slope of -3 and a y-intercept at the origin (0,0).
To graph this line, we can start by plotting the y-intercept at the origin. Then, using the slope, we can identify another point on the line. To find the second point, we can move one unit to the right along the x-axis, which will correspond to moving three units down along the y-axis.
Now, we can draw a dashed line through these two points to represent the inequality y ≥ -3x. The line should be dashed since the inequality includes a greater than or equal to sign. Finally, we can shade the area above the line to represent all the possible solutions.
Here is the graph of the inequality y ≥ -3x:
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-3 -2 -1 0 1 2 3
To translate the given phrase into an inequality and graph it, we need to follow a step-by-step process:
Step 1: Identify the variables
The variables mentioned in the phrase are x and y.
Step 2: Assign variables to their corresponding values
Let x represent a value and y represent another value.
Step 3: Translate the phrase into an algebraic equation
"The sum of 3 times x and 1 times y is greater than or equal to 0" can be translated into the equation: 3x + y ≥ 0.
Step 4: Graph the inequality
To graph this inequality, we'll start by representing the equation as a line on a coordinate plane. Since the inequality is "greater than or equal to 0," the line will be solid (not dashed) and include points on the line.
To graph this line, we'll use the slope-intercept form (y = mx + b) of the equation, where m is the slope and b is the y-intercept.
For the equation 3x + y ≥ 0, let's solve it for y:
y ≥ -3x
The slope of the line is -3, and the y-intercept is 0. So the line goes through the origin (0, 0) and has a slope of -3.
Now we'll plot some points on the line and choose points for testing:
- Pick a point to the left of the line (e.g., (-2, 0)).
- Pick a point to the right of the line (e.g., (2, 0)).
- Pick a point on the line (e.g., (0, 0)).
Plot these points on the graph and draw a line connecting them.
Since the inequality states "greater than or equal to," we shade the region either above or on the line. In this case, we'll shade the area above the line.
Lastly, label the graph appropriately and indicate that the line itself is included in the solution by using a solid line.
Note: The graphical representation will depend on the specific software or tool used.