The math club is selling T-shirts as a fund-raiser. There is a linear relationship between \(x\), the number of T-shirts sold, and \(y\), the profit in dollars from selling the T-shirts. When the club sells 6 shirts, it makes a profit of $10; when it sells 10 shirts, it makes a profit of $20. Which of the following equations gives the relationship between \(x\) and \(y\) ?

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You can try plugging in the given values. When \(x=6\), \(y=10\). When \(x=10\), \(y=20\). Only the last choice meets these conditions.

Given the points \((6,10)\) and \((10,20)\), we can find the slope.

$$ m = \frac{y_2-y_1}{x_2-x_1} $$ $$ m = \frac{20-10}{10-6} $$ $$ m = \frac{10}{4} = \frac{5}{2} $$

Use point-slope form to write the equation using one of the points and the slope:

$$ y-y_1 = m (x-x_1) $$ $$ y-10 = \frac{5}{2}(x-6) $$ $$ y-10 = \frac{5}{2}x - 15 $$ $$ \boxed{y= \frac{5}{2}x-5} $$