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.

Question

UpStudy AI · Accepted Answer

To write the equation in **point-slope form**, which is $$ y - y_1 = m(x - x_1) $$, follow these steps:

1. **Identify the Points:**
   - First point: $$ (2, 160) $$ where $$ x = 2 $$ seconds and $$ y = 160 $$ feet.
   - Second point: $$ (2.75, 220) $$ where $$ x = 2.75 $$ seconds and $$ y = 220 $$ feet.

2. **Calculate the Slope $$ m $$:**
   $$
   m = \frac{220 - 160}{2.75 - 2} = \frac{60}{0.75} = 80 \text{ feet per second}
   $$

3. **Choose One Point for the Equation:**
   Using the first point $$ (2, 160) $$:
   $$
   y - 160 = 80(x - 2)
   $$

**Final Equation:**
$$
y - 160 = 80(x - 2)
$$
The equation in point-slope form is $$ y - 160 = 80(x - 2) $$.

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 of the ball after seconds.

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Algebra Questions