Sally has been asked to write an equation for the line shown here, which approximates the sales data in the scatterplot.

She decides to use the second point, (2, 1600), and the last point, (10, 2100). What is the equation of the line in slope-intercept form?

To find the equation of a line in slope-intercept form \( y = mx + b \), we need to determine both the slope \( m \) and the y-intercept \( b \).

### Step 1: Find the slope \( m \)
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (2, 1600) \) and \( (10, 2100) \):
\[
m = \frac{2100 - 1600}{10 - 2} = \frac{500}{8} = 62.5
\]
So, the slope \( m = 62.5 \).

### Step 2: Use the slope and one point to find the y-intercept \( b \)
Now, we use the slope \( m = 62.5 \) and one of the points (we'll use \( (2, 1600) \)) to find the y-intercept \( b \) by substituting into the equation \( y = mx + b \).

Using \( y = 1600 \), \( x = 2 \), and \( m = 62.5 \):
\[
1600 = 62.5(2) + b
\]
\[
1600 = 125 + b
\]
\[
b = 1600 - 125 = 1475
\]

### Step 3: Write the equation
Now that we have both the slope \( m = 62.5 \) and the y-intercept \( b = 1475 \), the equation of the line is:
\[
y = 62.5x + 1475
\]

Would you like further clarification or details on any part of the process?

Here are some related questions to further explore this topic:
1. How do you interpret the slope in this context of sales data?
2. How does the y-intercept affect the interpretation of the sales data?
3. What would the line look like if the slope were negative?
4. Can the equation of this line be used to predict future sales? Why or why not?
5. How does the choice of points affect the accuracy of the line equation?

**Tip:** When plotting points for a line, using points that are far apart helps improve the accuracy of the slope.

Sally has been asked to write an equation for the line shown here, which approximates the sales data in the scatterplot. She decides to use the second point, (2, 1600), and the last point, (10, 2100). What is the equation of the line in slope-intercept form?

Learn how to find the equation of a line in slope-intercept form using the points (2, 1600) and (10, 2100) from a scatterplot. This guide covers key algebra concepts such as the slope formula and solving for the y-intercept. Suitable for students in Grades 8-10.

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