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 frac... 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.
Understand the Problem
The problem asks to determine the equation of the trend line shown in the scatter plot. The equation should be expressed in slope-intercept form (y = mx + b), and uses the two yellow points labeled on the image. The coefficients of the linear equation should be simplified.
Answer
$y = -\frac{1}{2}x + 6$
Answer for screen readers
$y = -\frac{1}{2}x + 6$
Steps to Solve
- Identify the coordinates of the two points
From the scatter plot, the coordinates of the two yellow points are $(0, 6)$ and $(8, 2)$.
- Calculate the slope ($m$) of the line
The formula for calculating the slope given two points $(x_1, y_1)$ and $(x_2, y_2)$ is:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Using the points $(0, 6)$ and $(8, 2)$:
$m = \frac{2 - 6}{8 - 0} = \frac{-4}{8} = -\frac{1}{2}$
- Determine the y-intercept ($b$)
Since we have the point $(0, 6)$, we know that the y-intercept is 6 because the x-coordinate is 0. Therefore, $b = 6$.
- Write the equation in slope-intercept form
The slope-intercept form of a linear equation is $y = mx + b$. We have $m = -\frac{1}{2}$ and $b = 6$. Substituting these values into the equation:
$y = -\frac{1}{2}x + 6$
$y = -\frac{1}{2}x + 6$
More Information
The equation represents a line with a negative slope, indicating that as $x$ increases, $y$ decreases. The y-intercept is 6, meaning the line crosses the y-axis at the point (0, 6).
Tips
A common mistake is to misread the coordinates of the points from the scatter plot or to incorrectly calculate the slope, for example, switching $x$ and $y$ values when computing $m$. Another common mistake is not simplifying the slope. Finally, forgetting to write the equation in the $y=mx+b$ form.
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