Question

Find the equation of the line through the point (10,-6) that is perpendicular to the line with equation -11x-18y=-2070

Answer 1

Step 1:

In this question, we are given the following:

Find the equation of the line through the point (10,-6) that is perpendicular to the line with equation

-11x-18y=-2070

Step 2:

The details of the solution are as follows:

`\begin{gathered} Given\text{ that:} \\ -11x\text{ - 18y = -2070} \\ We\text{ have that:} \\ -18y\text{ = 11x - 2070} \\ Divide\text{ both sides by -18, we have that:} \\ y\text{ = }\frac{11\text{ x}}{-18}\text{ }(-2070)/(-18) \\ Then,\text{ we have that:} \\ y\text{ = }\frac{-11\text{ x}}{18}\text{ + 115} \\ comparing\text{ this with:} \\ y\text{ = mx + c , then m = }(-11)/(18) \end{gathered}`
`\begin{gathered} For\text{ perpendicular lines, we have that:} \\ m_1m_2=\text{ -1} \\ Then,\text{ we have that:} \\ m_2=\text{ -1 x }(18)/(-11)=\text{ }(18)/(11) \\ Hence,\text{ m}_2=(18)/(11) \end{gathered}`
`\begin{gathered} We\text{ have the point:} \\ (\text{ 10 , - 6 \rparen} \\ Using\text{ the formulae:} \\ y\text{ - y}_1=\text{ m}_2\text{ \lparen x - x}_1) \end{gathered}`
`\begin{gathered} We\text{ have that:} \\ y\text{ - \lparen-6\rparen =}(18)/(11)\text{ \lparen x - 10 \rparen} \\ Multiply\text{ through by 11, we have that:} \\ 11y\text{ + 66 = 18x - 180} \\ Rearranging,\text{ we have that:} \\ 11y\text{ = 18x -180 - 66} \\ 11y\text{ = 18 x -246} \end{gathered}`

CONCLUSION:

The final answer is:

`11\text{ y = 18 x - 246}`