How do you graph #0.25x+3y>19# on the coordinate plane?
See a solution process below:
First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.
We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.
graph{((x4)^2+(y6)^20.125)((x16)^2+(y5)^20.125)(0.25x+3y19)=0 [30, 30, 15, 15]}
Now, we can shade the right/upper side of the line. The boundary line needs to be changed to a dashed line because the inequality operator does not contain an "or equal to" clause.
graph{(0.25x+3y19) > 0 [30, 30, 15, 15]}
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To graph the inequality (0.25x + 3y > 19) on the coordinate plane, follow these steps:

Start by graphing the boundary line (0.25x + 3y = 19). To do this, first find two points that lie on the line. You can choose any convenient values for (x) and solve for (y), or vice versa. For simplicity, let's choose (x = 0) and (y = 0):
When (x = 0): (0.25(0) + 3y = 19)
(3y = 19)
(y = \frac{19}{3} \approx 6.33)When (y = 0): (0.25x + 3(0) = 19)
(0.25x = 19)
(x = \frac{19}{0.25} = 76)So, the two points on the line are ((0, \frac{19}{3})) and ((76, 0)).

Plot these points on the coordinate plane and draw a straight line passing through them. This line represents the boundary of the inequality.

Since the inequality is (0.25x + 3y > 19), we need to determine which side of the boundary line to shade. To do this, choose a point not on the line (usually the origin ((0,0))) and substitute its coordinates into the inequality. If the inequality is true, shade the region containing that point; if not, shade the other region.
Let's test the point ((0,0)): (0.25(0) + 3(0) > 19)
(0 > 19)Since (0 > 19) is false, shade the region not containing the origin.

Finally, draw the shaded region on the side of the boundary line determined in step 3. This shaded region represents the solution to the inequality (0.25x + 3y > 19).
So, on the coordinate plane, you'll graph the boundary line (0.25x + 3y = 19) and shade the region above or below the line, depending on which side satisfies the inequality (0.25x + 3y > 19).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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