Lines Question 2

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 $y$ ?

y=\dfrac{2}{5}x+2

y=\dfrac{2}{5}x+\dfrac{38}{5}

y=\dfrac{5}{2}x+4

y=\dfrac{5}{2}x+5

y=\dfrac{5}{2}x-5

Approach 1

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.

Approach 2

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}