Determine the type of boundary line and shading for the graph of the inequality 3x + y (greater than or equal to) 10.
A) Dashed line with shading on the side that includes the origin.
B) Solid line with shading on the side that does not include the origin.
C) Dashed line with shading on the side that does not include the origin.
D) Solid line with shading on the side that includes the origin.
is it b
sorry it was an honest mistake pls help me though
'Sokay! I'm not a math tutor. Someone will log on and help you, I'm sure. :)
ok thx so much
The >= condition indicates you will need a solid line, because
3x+y = 10
is part of the solution. So, B and D are the only possibilities.
Now draw that line. Since you want
3x+y >= 10
you shade the part of the plane above the line, as that's where the sum of 3x+y is more than 10.
So, since (0,0) is below the line (0+0 < 10) you want to shade the part away from the origin: (B)
To determine the type of boundary line and shading for the graph of the inequality 3x + y ≥ 10, you need to follow these steps:
Step 1: Rewrite the inequality in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
To do this, subtract 3x from both sides:
y ≥ -3x + 10
Step 2: Determine the slope and y-intercept of the line.
In this case, the slope is -3 and the y-intercept is 10.
Step 3: Plot the y-intercept on the graph.
The y-intercept is the value of y when x = 0, so plot the point (0, 10) on the graph.
Step 4: Find another point on the line.
To find another point, you can choose any value for x and substitute it into the equation to solve for y. Let's choose x = 2:
y ≥ -3(2) + 10
y ≥ -6 + 10
y ≥ 4
So, another point on the line is (2, 4).
Step 5: Draw the line.
Since the inequality is inclusive of the equal sign (≥), the line should be solid.
Step 6: Determine the shading.
For this inequality, the shading should be on the side that includes the origin because it is greater than or equal to 10.
Based on these steps, the correct answer is D) Solid line with shading on the side that includes the origin.