To determine the equation of the linear relation in point-slope form, we need to follow these steps:
1. Identify the coordinates of the given points:
[tex]\[
(x_1, y_1) = (6, 4) \quad \text{and} \quad (x_2, y_2) = (18, -4)
\][/tex]
2. Calculate the slope [tex]\( m \)[/tex] using the formula:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substituting the given coordinates:
[tex]\[
m = \frac{-4 - 4}{18 - 6} = \frac{-8}{12} = -\frac{2}{3} \approx -0.6666666666666666
\][/tex]
3. Using the point-slope form [tex]\( y - y_1 = m(x - x_1) \)[/tex], and substituting [tex]\( m = -\frac{2}{3} \)[/tex], [tex]\( x_1 = 6 \)[/tex], and [tex]\( y_1 = 4 \)[/tex]:
[tex]\[
y - 4 = -\frac{2}{3}(x - 6)
\][/tex]
Thus, the equation of the line in point-slope form is:
[tex]\[
y - 4 = -\frac{2}{3}(x - 6)
\][/tex]
This represents the linear relation passing through the points [tex]\((6, 4)\)[/tex] and [tex]\((18, -4)\)[/tex].
