Question

Find the equation of the line perpendicular to y=4/3x+1 through point (-7,-2)

Answer 1

Given the question in the question tab, the following are the steps to find the equation

Step 1: Write the equation of the initial line and get the slope by comparing with the general line equation.

`\begin{gathered} y=mx+c \\ \text{where the coefficient of }x\text{ is the slope (m)} \\ y=(4)/(3)x+1 \\ m=(4)/(3) \end{gathered}`

Step 2: Get the slope of the perpendicular line

The slopes of two perpendicular lines are negative reciprocals of each other. This means that if a line is perpendicular to a line that has slope m, then the slope of the line is -1/m.

`\begin{gathered} m=(4)/(3) \\ m_{\text{perpendicular}}=-(1)/((4)/(3)) \\ m_{\text{perpendicular}}=-1*(3)/(4) \\ m_{\text{perpendicular}}=-(3)/(4) \end{gathered}`

Step 3: Get the y-intercept of the perpendicular line using the general equation of a line

`\begin{gathered} y=mx+b \\ (x,y)=(-7,-2),m=-(3)/(4) \\ -2=-(3)/(4)(-7)+b \\ -2=(21)/(4)+b \\ b=-2-(21)/(4) \\ b=-(8)/(4)-(21)/(4) \\ b=(-8-21)/(4) \\ b=-(29)/(4) \end{gathered}`

Step 4: We compute the final equation of the line perpendicular to y=4/3x+1 through point (-7,-2)​

`\begin{gathered} y=mx+b \\ y=-(3)/(4)x+(-(29)/(4)) \\ y=-(3)/(4)x-(29)/(4) \end{gathered}`

Hence, the equation of the line perpendicular to y=4/3x+1 through point (-7,-2)​ is:

`y=-(3)/(4)x-(29)/(4)`