Question

Find the slope-intercept form of the trend line using these points:

(4, 16)
(6, 14)

Answer:
y =

Answer 1

To find the slope-intercept form of the trend line using the given points \((4, 16)\) and \((6, 14)\), we first need to calculate the slope \(m\) using the formula:

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

Substituting the coordinates of the points \((x_1, y_1) = (4, 16)\) and \((x_2, y_2) = (6, 14)\):

\[
m = \frac{14 - 16}{6 - 4} = \frac{-2}{2} = -1
\]

Now that we know the slope \(m = -1\), we can use point-slope form of a line, which is given by:

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

Using the point \((4, 16)\):

\[
y - 16 = -1(x - 4)
\]

Expanding this equation:

\[
y - 16 = -x + 4
\]

Adding 16 to both sides gives:

\[
y = -x + 4 + 16
\]

Simplifying:

\[
y = -x + 20
\]

Thus, the slope-intercept form of the trend line is:

\[
\boxed{y = -x + 20}
\]