Question

Write an equation in slope-intercept form of the trend line
starting point: (0,20)
two points:(15,40) and (30,60)
ending point: around (40,73)

Answer 1

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

### Step 1: Calculate the slope \(m\)

We can use the two points (15, 40) and (30, 60) to calculate the slope:

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

Substituting in the values from the points:

\[
m = \frac{60 - 40}{30 - 15} = \frac{20}{15} = \frac{4}{3}
\]

### Step 2: Use the point-slope form to find the equation

We can use the point-slope form of the equation, which is:

\[
y - y_1 = m(x - x_1)
\]

Using the starting point (0, 20):

\[
y - 20 = \frac{4}{3}(x - 0)
\]

This simplifies to:

\[
y - 20 = \frac{4}{3}x
\]

Adding 20 to both sides gives us the slope-intercept form:

\[
y = \frac{4}{3}x + 20
\]

### Final Equation

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

\[
y = \frac{4}{3}x + 20
\]

### Verification with the End Point

To verify that the end point (40, 73) is approximately on this line:

Substituting \(x = 40\) into the equation:

\[
y = \frac{4}{3}(40) + 20 = \frac{160}{3} + 20 = \frac{160}{3} + \frac{60}{3} = \frac{220}{3} \approx 73.33
\]

This is close to 73, confirming that the trend line is consistent with the provided points.