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The table you have provided contains two columns of values, \( x \) and \( y \), as follows:

\[
\begin{array}{c|c}
x & y \\
\hline
15 & 100 \\
20 & 115 \\
25 & 130 \\
30 & 145 \\
35 & 160 \\
\end{array}
\]

This data seems to represent a linear relationship between \( x \) and \( y \). To find the equation of the line that models this relationship, we can use the slope-intercept form of a line:

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Find the slope \( m \)

The slope of a line is given by the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using two points from the table, say \( (15, 100) \) and \( (20, 115) \), we can compute the slope:

\[
m = \frac{115 - 100}{20 - 15} = \frac{15}{5} = 3
\]

### Step 2: Find the y-intercept \( b \)

Now that we know the slope \( m = 3 \), we can use one of the points to solve for \( b \). Using the point \( (15, 100) \):

\[
100 = 3(15) + b
\]

Solving for \( b \):

\[
100 = 45 + b \implies b = 100 - 45 = 55
\]

### Step 3: Equation of the line

Now that we have both the slope \( m = 3 \) and the intercept \( b = 55 \), the equation of the line is:

\[
y = 3x + 55
\]

This equation models the relationship between \( x \) and \( y \) in the table.

Would you like further details or clarifications?

Here are five follow-up questions to explore this topic:

1. What would be the predicted \( y \)-value when \( x = 40 \) using the equation \( y = 3x + 55 \)?
2. How can we determine if a relationship between two variables is truly linear?
3. How would the graph of the equation \( y = 3x + 55 \) look?
4. How can you calculate the slope if the relationship between \( x \) and \( y \) is not linear?
5. What happens to the line if we change the slope or intercept in the equation?

**Tip:** When trying to fit data to a linear model, always verify the consistency of the slope between multiple pairs of points to ensure the relationship is linear.

Find the equation of the line that models the relationship between x and y using the table of values: x = [15, 20, 25, 30, 35] and y = [100, 115, 130, 145, 160].

Discover how to find the linear equation from the table with x-values [15, 20, 25, 30, 35] and corresponding y-values [100, 115, 130, 145, 160]. Learn about the slope-intercept form, how to calculate the slope, and determine the y-intercept. Suitable for Grades 8-10 students.

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