https://file.aiquickdraw.com/mathbot/file/1727285790382ktjggq6e.jpg

nilai tofel 2014 → 382
2019 → 552
2024 → 522
 2029 → ... 
a. cari persamaan linear dari data tersebut
b. kalau tidak dilakukan tindakan perbaikan berapa nilai TOFEL di tahun 2029

We are asked to find a linear equation for the given data and then predict the TOEFL score in 2029 if no intervention is done.

We are provided with the following data points:

- 2014: 382
- 2019: 552
- 2024: 522
- 2029: ?

### Part a: Finding the Linear Equation

Let's assume the relation between TOEFL score (\(y\)) and year (\(x\)) is linear, so we can express it as:

\[
y = mx + c
\]

Where:
- \(m\) is the slope (rate of change in TOEFL score per year).
- \(c\) is the intercept.

We will calculate the slope \(m\) using two known points, (2014, 382) and (2019, 552):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{552 - 382}{2019 - 2014}
\]

Then, we can use one of the points to find \(c\).

Once we have the equation, we can answer part b by plugging \(x = 2029\) into the equation to predict the TOEFL score.

Let me calculate the slope and the equation now.### Part a: The linear equation derived from the data is:

\[
y = 34x - 68094
\]

Where \(y\) represents the TOEFL score and \(x\) is the year.

### Part b: Predicting the TOEFL score for 2029

Using the equation \(y = 34x - 68094\), when \(x = 2029\), the predicted TOEFL score is:

\[
y = 34(2029) - 68094 = 892
\]

Thus, if no action is taken, the TOEFL score in 2029 is predicted to be **892**.

Would you like further details on the calculations or assistance with any related questions?

Here are 5 related questions you might want to explore:
1. How does the slope of a linear equation affect the growth rate in predictions?
2. What is the significance of the intercept in a linear equation?
3. How can we use more data points to improve the accuracy of the linear model?
4. What other types of regression could better fit the data besides linear regression?
5. How do external factors influence TOEFL scores over time, and how can we model this?

**Tip:** When modeling with data, always check if the relationship is truly linear. Sometimes more complex models like polynomial regression might fit better.

Cari persamaan linear dari data berikut dan tentukan berapa nilai TOEFL di tahun 2029 jika tidak dilakukan tindakan perbaikan.

Learn how to find the linear equation from TOEFL scores in 2014, 2019, and 2024, and predict the score for 2029 if no intervention is taken. This problem uses slope-intercept form and is suitable for students in Grades 10-12.

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