Question

Write an equation in slope-intercept form of the trend line when the trend line passes through points 15 on the x axis and 40 on the y axis

Answer 1

To write 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 \(b\).

Given the two points:
- Point 1: \((15, 0)\) (where the line intersects the x-axis)
- Point 2: \((0, 40)\) (where the line intersects the y-axis)

1. **Find the slope \(m\):**
The slope \(m\) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, let \((x_1, y_1) = (15, 0)\) and \((x_2, y_2) = (0, 40)\):
\[
m = \frac{40 - 0}{0 - 15} = \frac{40}{-15} = -\frac{8}{3}
\]

2. **Use the slope and one of the points to find the y-intercept \(b\):**
We can use the point \((0, 40)\) to find \(b\) directly, but since we already see that this point represents the y-intercept, we know that \(b = 40\).

3. **Write the equation:**
Now that we have \(m = -\frac{8}{3}\) and \(b = 40\), we can write the equation in slope-intercept form:
\[
y = -\frac{8}{3}x + 40
\]

Thus, the equation of the trend line is:

\[
y = -\frac{8}{3}x + 40
\]