Question

write an equation in slope intercept form of a trend line if two points are 5,3 and 29,1

Answer 1

To find the equation of the trend line in slope-intercept form \( y = mx + b \), we need to find the slope \( m \) and the y-intercept \( b \) using the given points (5, 3) and (29, 1).

1. **Calculate the slope \( m \)** using the formula:

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

Let \((x_1, y_1) = (5, 3)\) and \((x_2, y_2) = (29, 1)\):

\[
m = \frac{1 - 3}{29 - 5} = \frac{-2}{24} = -\frac{1}{12}
\]

2. **Use the slope and one of the points to find \( b \)**. We can use the point (5, 3):

\[
y = mx + b \implies 3 = -\frac{1}{12}(5) + b
\]

Calculating:

\[
3 = -\frac{5}{12} + b
\]

To isolate \( b \), add \(\frac{5}{12}\) to both sides:

\[
3 + \frac{5}{12} = b
\]

Convert 3 to a fraction with a denominator of 12:

\[
3 = \frac{36}{12} \implies \frac{36}{12} + \frac{5}{12} = b
\]

Thus,

\[
b = \frac{41}{12}
\]

3. **Write the final equation**:

Now that we have \( m = -\frac{1}{12} \) and \( b = \frac{41}{12} \), the equation of the trend line in slope-intercept form is:

\[
y = -\frac{1}{12}x + \frac{41}{12}
\]