7. Alice graphs the relationship between \( x \), the number of years an athlete has been playing basketball, and \( y \), their average number of baskets per game. Her graph goes through the points (8,8) and \( (4,5) \). Which equation represents the graph? \( \begin{array}{ll}\text { (A) } y=\frac{3}{4} x+2 & \text { (C) } y=\frac{4}{3} x+\frac{31}{3} \\ \text { (B) } y=-\frac{3}{4} x-2 & \text { (D) } y=\frac{4}{3} x-\frac{1}{3}\end{array} \)

To determine which equation represents the relationship between \( x \) and \( y \), we first need to find the slope \( m \) of the line passing through the points \( (8,8) \) and \( (4,5) \). The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 8}{4 - 8} = \frac{-3}{-4} = \frac{3}{4} \] Now we use the point-slope form of the equation (or slope-intercept form) with one of the points, say \( (4, 5) \): \[ y - 5 = \frac{3}{4}(x - 4) \] Solving this gives: \[ y - 5 = \frac{3}{4}x - 3 \quad \Rightarrow \quad y = \frac{3}{4}x + 2 \] Therefore, the correct answer is option (A) \( y=\frac{3}{4} x+2 \). When working with graphs, remember that the slope indicates the steepness, and the intercept is where the line crosses the y-axis. Keep track of your calculations to avoid common mistakes like misplacing signs or confusion in slope calculations! Always double-check with two points if you're unsure about the slope derived.