### Equations of special straight lines

Question Sample Titled 'Equations of special straight lines'

 (a)  The equation of a horizontal line passing through ${\left({0},{k}\right)}$ is given by: ${y}$ $={k}$ (b) The equation of a vertical line passing through ${\left({h},{0}\right)}$ is given by: ${x}$ $={h}$ (c) If a straight line ${L}$ passes through the origin and has slope${m}$, the equation of ${L}$ is given by: ${y}$ $={m}{x}$

 Example In the figure, ${L}_{{1}}$ and ${L}_{{2}}$ are horizontal and vertical lines resepectively. ${P}$ is the intersection of the two straight lines. Find the equations of ${L}_{{1}}$ and ${L}_{{2}}$ . 

${x}$${y}$${L}_{{1}}$${L}_{{2}}$${P}{\left({3},{4}\right)}$

 Solution ∵ ${L}_{{1}}$ is a horizontal line. ∴ The equation of ${L}_{{1}}$ is ${y}$ $={4}$ . ∵ ${L}_{{2}}$ is a vertical line. ∴ The equation of ${L}_{{1}}$ is ${x}$ $={3}$ .

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