Questions: What is the equation of the trend line in the scatter plot? Use the two yellow points to write the equation in slope-intercept form. Write any coefficients as integers, proper fractions, or improper fractions in simplest form.

What is the equation of the trend line in the scatter plot? Use the two yellow points to write the equation in slope-intercept form. Write any coefficients as integers, proper fractions, or improper fractions in simplest form.
Transcript text: What is the equation of the trend line in the scatter plot? Use the two yellow points to write the equation in slope-intercept form. Write any coefficients as integers, proper fractions, or improper fractions in simplest form.
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Solution

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Solution Steps

Step 1: Identify the Coordinates of the Yellow Points

The yellow points on the scatter plot are at coordinates (3, 1) and (6, 9).

Step 2: Calculate the Slope (m)

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substitute the coordinates: \[ m = \frac{9 - 1}{6 - 3} = \frac{8}{3} \]

Step 3: Use the Slope-Intercept Form

The slope-intercept form of a line is: \[ y = mx + b \]

We already have \( m = \frac{8}{3} \). Now, we need to find \( b \) (the y-intercept). Use one of the points, say (3, 1), and substitute into the equation: \[ 1 = \frac{8}{3}(3) + b \] \[ 1 = 8 + b \] \[ b = 1 - 8 \] \[ b = -7 \]

Final Answer

The equation of the trend line is: \[ y = \frac{8}{3}x - 7 \]

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