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
Share
To determine the equation of the trend line in slope-intercept form (y = mx + b) using two points from the scatter plot, we first need the coordinates of those two yellow points, which I’ll denote as (x₁, y₁) and (x₂, y₂).
### Step-by-step process:
1. Calculate the slope (m):
The slope (m) is calculated using the formula:
[
m = frac{y₂ – y₁}{x₂ – x₁}
]
2. Use one of the points to solve for b (the y-intercept):
Once you have the slope, plug one of the points into the slope-intercept form equation to solve for b:
[
y₁ = mx₁ + b implies b = y₁ – mx₁
]
3. Write the equation:
Substitute m and b back into the slope-intercept form equation (y = mx + b).
### Example:
If the two yellow points are (1, 2) and (3, 4):
1. The slope m:
[
m = frac{4 – 2}{3 – 1} = frac{2}{2} = 1
]
2. Using the point (1, 2):
[
2 = 1(1