Question

write an equation in slope intercept form of a trend line if two points on the trend line is 16,4 and 18.7

Answer 1

To find the equation of a trend line in slope-intercept form, we first need to calculate the slope (m) using the two points provided: (16, 4) and (18, 7).

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Substituting the coordinates of the points into the formula:

\[
m = \frac{7 - 4}{18 - 16} = \frac{3}{2}
\]

Now that we have the slope, we can use one of the points (let’s use (16, 4)) to find the y-intercept (b) using the slope-intercept form of a line:

\[
y = mx + b
\]

We can substitute \( m \) and the coordinates of the point into this equation. Using the point (16, 4):

\[
4 = \frac{3}{2} \cdot 16 + b
\]

Calculating:

\[
4 = 24 + b
\]

Now, isolate \( b \):

\[
b = 4 - 24 = -20
\]

Now we can write the equation in slope-intercept form:

\[
y = \frac{3}{2}x - 20
\]

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

\[
y = \frac{3}{2}x - 20
\]