Problem
Line $l_{1}$ has equation $3 x+5 y-14=0$ and crosses the $y$-axis at point $Y$. a) Find the coordinates of point $Y$. b) Find the obtuse angle thât line $l_{1}$ makes with the $y$-axis. Line $l_{2}$ is perpendicular to line $l_{1}$ and the two lines intersect at $(8,-2)$. c) Find the equation of line $l_{2}$. Give your answer in the form $a x+b y+c=$ () where $a, b$ and $c$ are integers.
Solution
Step 1 ：Substitute x = 0 into the equation of the line to find the y-coordinate of point Y.
Step 2 ：The equation of the line is \(3x + 5y - 14 = 0\).
Step 3 ：Substituting x = 0 gives \(5y - 14 = 0\).
Step 4 ：Solving for y gives \(y = \frac{14}{5}\).
Step 5 ：\(\boxed{The coordinates of point Y are (0, \frac{14}{5})}\).
