Question

write an equation in slope intercept form of a trend line if two points are 5,3 and 29,1 no fractions

Answer 1

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

**Step 1: Calculate the slope (m)**

The formula for the slope \( m \) between 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 (5, 3) (where \( x_1 = 5 \) and \( y_1 = 3 \)) and (29, 1) (where \( x_2 = 29 \) and \( y_2 = 1 \)):

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

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

Now that we have the slope \( m = -\frac{1}{12} \), we can use one of the points to solve for \( b \). We can use the point (5, 3):

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

Now solve for \( b \):

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

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

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

To add these two numbers together, convert 3 to have a denominator of 12:

\[
3 = \frac{36}{12}
\]
\[
b = \frac{36}{12} + \frac{5}{12} = \frac{41}{12}
\]

**Step 3: Write the equation in slope-intercept form**

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

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

However, since you requested no fractions, we can multiply the entire equation by 12 to eliminate the denominators:

\[
12y = -x + 41
\]

Rearranging gives:

\[
x + 12y = 41
\]

Thus, while in standard form we have:

\[
x + 12y = 41
\]

If you want it strictly in slope-intercept form:

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

But if you prefer whole numbers only, use:

**Final Result:**

\[
x + 12y = 41
\]