Question

The trend line starts at 0, 25 and ends at 10, 75
Write an equation in slope-intercept form of the trend line.

Answer 1

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

### Step 1: Find the slope (m)

The slope \( m \) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Given the points \( (x_1, y_1) = (0, 25) \) and \( (x_2, y_2) = (10, 75) \):

\[
m = \frac{75 - 25}{10 - 0} = \frac{50}{10} = 5
\]

### Step 2: Use the slope to find the y-intercept (b)

Now that we have the slope, we can use one of the points to solve for the y-intercept \( b \) in the equation \( y = mx + b \). We can use the point \( (0, 25) \):

\[
y = mx + b
\]
\[
25 = 5(0) + b
\]
\[
25 = b
\]

### Step 3: Write the equation

Now we can write the equation of the trend line:

\[
y = 5x + 25
\]

Thus, the equation of the trend line in slope-intercept form is:

\[
y = 5x + 25
\]