Question

which point on the y - axis is on the line that passes through point r and is parallel to line pq?
(4,0)
(\frac{2}{3},0)
(0,4)
(0,\frac{2}{3})

Explanation:

Step1: Find the slope of line PQ

Let \(P(-3,3)\) and \(Q(-1,-3)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
So, \(m_{PQ}=\frac{-3 - 3}{-1-(-3)}=\frac{-6}{2}=-3\).

Step2: Use the point - slope form

Since the line passes through \(R(1,-1)\) and is parallel to \(PQ\) (so it has the same slope \(m = - 3\)). The point - slope form is \(y - y_1=m(x - x_1)\).
\(y+1=-3(x - 1)\), which simplifies to \(y=-3x + 2\).
When \(x = 0\), \(y=2\).

Answer:

\((0,2)\)