Question

Carlos plays an arcade game. the scatter plot shows his score and the number of minutes he plays. A good line of fit is drawn through the points (6,50) and (12,80)
Carlos plays the game for 25 minutes. use the equation of the line of fit to predict his score?

Answer 1

To find Carlos's predicted score after playing the game for 25 minutes, we first need to determine the equation of the line of fit that passes through the points (6, 50) and (12, 80).

1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where (x1, y1) = (6, 50) and (x2, y2) = (12, 80).

\[
m = \frac{80 - 50}{12 - 6} = \frac{30}{6} = 5
\]

2. **Use the point-slope form** to write the equation of the line. Since we have the slope and a point (let's use (6, 50)), we can use the point-slope form of the equation:
\[
y - y_1 = m(x - x_1)
\]
Plugging in the values:
\[
y - 50 = 5(x - 6)
\]

3. **Simplify the equation**:
\[
y - 50 = 5x - 30
\]
\[
y = 5x + 20
\]

4. **Now, use this equation to predict the score for 25 minutes**:
\[
y = 5(25) + 20
\]
\[
y = 125 + 20
\]
\[
y = 145
\]

Thus, predicting Carlos's score when he plays for 25 minutes gives us **145**.