Question - Analysis of Coordinates and Linear Equation of Points in Cartesian Plane

Given point Q(8, k) and point S(-6, 0), it is known that line PQ is parallel to the x-axis.

(a) Since PQ is parallel to the x-axis, the y-coordinates of points P and Q are equal, which means the y-coordinate of point Q is k = 0 (the same as point S).

\(k = 0\)

(b) To find the equation of line PS, we can calculate the slope (m) using the coordinates of points P and S:

\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 0}{-6 - 8}\)

Since the change in y is 0 (the line is horizontal), the slope is:

\(m = 0\)

The general equation of a line is \(y = mx + b\). Since the slope m = 0, the equation simplifies to

\(y = b\)

To find b, we use the fact that the line passes through point S(-6, 0):

\(0 = 0 \cdot (-6) + b\)

\(b = 0\)

The equation of line PS is therefore \(y = 0\).