The lines ${\ell }_1$ and ${\ell }_2$ have equations

1. Verify that $(4,2)$ lies on both ${\ell }_1$ and ${\ell }_2.$

2. Prove that the lines ${\ell }_1$ and ${\ell }_2$ are perpendicular.

3. Find the area of the triangle formed by ${\ell }_1,{\ell }_2$ and the $y$-axis.

For (a), just substitute the point into both lines and make sure the equation is satisfied.

For (b), put each line into the form $y=mx+c$ and demonstrate that $m_1{m}_2=-1$

Draw a picture. You can use a horizontal and vertical line to find the area, which is easier than calculating lengths of the diagonal lines.