To graph the inequality 6x - 3y ≥ 15, we need to plot the corresponding equation 6x - 3y = 15, which is the equation of the equality.
First, let's solve the equation for y.
6x - 3y = 15
-3y = -6x + 15
y = 2x - 5
Next, we can graph the equation y = 2x - 5, which is a straight line with a slope of 2 and a y-intercept of -5.
Now, let's determine which region to shade as the solution to the inequality 6x - 3y ≥ 15. To do this, we can pick a point not on the line and substitute it into the inequality to check if it satisfies the inequality or not.
Let's pick the point (0,0).
6(0) - 3(0) ≥ 15
0 ≥ 15
Since 0 is not greater than or equal to 15, the point (0,0) is not a solution for the inequality.
Since we want to find the region where the inequality is true, we need to shade the region that does not include the point (0,0). In this case, it is the region above the line y = 2x - 5.
6x−3y≥15
9 answers
What is the equation of the boundary line of the graph of
The equation of the boundary line of the graph of 6x - 3y ≥ 15 is 6x - 3y = 15.
are you sure
I apologize for the confusion in my previous response. You're right, the equation of the boundary line for the graph of 6x - 3y ≥ 15 is 6x - 3y = 15. Thank you for pointing that out, and I apologize for any confusion caused.
what steps you take to get the answer?
To find the equation of the boundary line for the graph of 6x - 3y ≥ 15, you need to follow these steps:
1. Start with the given inequality: 6x - 3y ≥ 15.
2. Rewrite the inequality as an equation by removing the inequality sign and replacing it with an equals sign. The equation will be: 6x - 3y = 15.
3. This equation represents a line. To determine the equation of the line, you need to solve it for y.
4. Begin by isolating the y term by subtracting 6x from both sides of the equation: -3y = -6x + 15.
5. Next, divide the entire equation by -3 to solve for y: y = 2x - 5.
6. The resulting equation, y = 2x - 5, is now in slope-intercept form (y = mx + b), where m represents the slope of the line (2 in this case) and b represents the y-intercept (-5 in this case).
Thus, the equation of the boundary line for the graph of 6x - 3y ≥ 15 is y = 2x - 5.
1. Start with the given inequality: 6x - 3y ≥ 15.
2. Rewrite the inequality as an equation by removing the inequality sign and replacing it with an equals sign. The equation will be: 6x - 3y = 15.
3. This equation represents a line. To determine the equation of the line, you need to solve it for y.
4. Begin by isolating the y term by subtracting 6x from both sides of the equation: -3y = -6x + 15.
5. Next, divide the entire equation by -3 to solve for y: y = 2x - 5.
6. The resulting equation, y = 2x - 5, is now in slope-intercept form (y = mx + b), where m represents the slope of the line (2 in this case) and b represents the y-intercept (-5 in this case).
Thus, the equation of the boundary line for the graph of 6x - 3y ≥ 15 is y = 2x - 5.
6x−3y≥15
Write in Slope-Intercept Form
Write in Slope-Intercept Form
To write the inequality 6x - 3y ≥ 15 in slope-intercept form, we need to rewrite it as y ≥ mx + b, where m represents the slope and b represents the y-intercept.
First, let's isolate the y term:
6x - 3y ≥ 15
Next, subtract 6x from both sides:
-3y ≥ -6x + 15
Now, divide both sides by -3 (note that we must reverse the inequality symbol when dividing by a negative number):
y ≤ 2x - 5
Therefore, the inequality 6x - 3y ≥ 15 can be written in slope-intercept form as y ≤ 2x - 5.
First, let's isolate the y term:
6x - 3y ≥ 15
Next, subtract 6x from both sides:
-3y ≥ -6x + 15
Now, divide both sides by -3 (note that we must reverse the inequality symbol when dividing by a negative number):
y ≤ 2x - 5
Therefore, the inequality 6x - 3y ≥ 15 can be written in slope-intercept form as y ≤ 2x - 5.