To find the equation of the trend line in slope-intercept form \(y = mx + b\), we need to determine the slope \(m\) and the y-intercept \(b\).
From the points you provided:
- Point 1: (0, 25)
- Point 2: (1, 30)
- Point 3: (2, 35)
- Point 4: (7, 60)
- Point 5: (10, 75)
Step 1: Calculate the slope (m)
The slope \(m\) can be calculated using any two points. Let's use points (1, 30) and (2, 35):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{35 - 30}{2 - 1} = \frac{5}{1} = 5 \]
Step 2: Use one point to find the y-intercept (b)
We can use point (0, 25) to find \(b\). Using the slope-intercept form:
\[ y = mx + b \ 25 = 5(0) + b \ b = 25 \]
Final Equation
Now that we have \(m\) and \(b\), we can write the equation of the trend line:
\[ y = 5x + 25 \]
So, in slope-intercept form, the equation is:
\[ y = 5x + 25 \]