After 2 seconds on a penalty kick in soccer, the ball travels 160 feet. After 2.75 seconds on the same kick, the ball travels 220 feet. Write an equation in point-slope form to represent the distance \( y \) of the ball after \( x \) seconds.

To find the point-slope form of the equation representing the distance of the ball after a given time, we first identify two points based on the information given: (2, 160) and (2.75, 220). Next, we need to calculate the slope \( m \) of the line connecting these two points using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the values: \[ m = \frac{220 - 160}{2.75 - 2} = \frac{60}{0.75} = 80 \] Now we can use one of the points (let's choose (2, 160)) and apply the point-slope form \( y - y_1 = m(x - x_1) \): \[ y - 160 = 80(x - 2) \] So, the equation in point-slope form representing the distance \( y \) of the ball after \( x \) seconds is: \[ y - 160 = 80(x - 2) \] This equation describes the relationship between time and distance for the penalty kick in soccer!