To find the equation that describes the direct variation function between total earnings \( E \) and hours worked \( h \), we can use the provided points that the line passes through. The coordinates given are:
- (0, 0)
- (4, 30)
- (8, 60)
- (12, 90)
In a direct variation, the relationship can be expressed as:
\[ E = kh \]
where \( k \) is the constant of variation. To find \( k \), we can use any of the non-zero points.
Using the point (4, 30):
\[ E = kh \implies 30 = k(4) \implies k = \frac{30}{4} = 7.5 \]
Now we can write the equation:
\[ E = 7.5h \]
To confirm, let's check with another point, for example, (8, 60):
\[ E = 7.5h \implies 60 = 7.5(8) \implies 60 = 60 \quad \text{(True)} \]
And for (12, 90):
\[ E = 7.5h \implies 90 = 7.5(12) \implies 90 = 90 \quad \text{(True)} \]
Thus, the correct equation that describes this direct variation function is:
\[ \boxed{E = 7.5h} \]
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