3. The graph of a proportional relationship goes through the point \( (8,40) \). Write an equation to represent the proportional relationship.
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In a proportional relationship, the equation can be expressed as \( y = kx \), where \( k \) is the constant of proportionality. To find \( k \), we can use the coordinates of the point given, \( (8, 40) \). By substituting into the equation, we have \( 40 = k(8) \), which means \( k = 5 \). Hence, the equation representing the proportional relationship is \( y = 5x \). Keep in mind, whenever you're dealing with proportional relationships, the ratio between the two variables is constant. In this case, for every increase of 1 in \( x \), \( y \) increases by 5, which is quite handy for predicting outcomes in real life, like budgeting or scaling recipes!
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