The amount Ben earns, [tex]y[/tex], varies directly with the number of hours he works, [tex]x[/tex], as shown in the graph.
1. Write a direct variation equation.
2. Identify the constant of variation and interpret its meaning.
Answer (3)
Not as complicated if you understand direct variation. The standard set up for direct variation is y=kx , which happens to be the case here. K stands for constant, which is what it is asking for. The constant is the ratio of y/x in direct variation and I can not solve that without seeing the graph, but the meaning of the constant of variation in this situation is The amount Ben earns per hour. Or in general The constant number multiplied by x to get y in the ratio between x and y in a direct variation situation.
The direct variation equation is based on the formula y = kx, where k is the constant of variation, showing the rate that y changes with respect to x.
For direct variation, Ben earns a consistent amount per hour worked, represented by k.
If an initial amount is included, the equation adjusts to account for it.
If the amount Ben earns (y) varies directly with the number of hours he works (x), this means that there is a linear relationship between y and x.
To write a direct variation equation, we rely on the formula y = kx , where k is the constant of variation.
The constant of variation represents the rate that y changes with respect to x.
Using the information provided from a graph or table, if it is given that for example, Ben earns $55 per hour, the direct variation equation would be y = 55x. Here, 55 is the constant of variation, meaning for every hour Ben works, he earns $55.
If a y-intercept is given, like $75, it does not fit the model of direct variation, as direct variation assumes that Ben earns nothing when he doesn't work ( x=0 ).
In such a case, the equation incorporates the initial amount plus the amount earned from working, which would be y = 55x + 75.
The direct variation equation for Ben's earnings is y = k x , where k represents his hourly wage. The constant of variation, k , indicates how much Ben earns per hour, for example, $20 per hour. This means for every hour worked, Ben's total earnings increase by that same amount.
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