Respuesta :
SOLUTION
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.
[tex]\begin{gathered} y=mx+c \\ \text{where the coefficient of }x\text{ is the slope (m)} \\ y=\frac{4}{3}x+1 \\ m=\frac{4}{3} \end{gathered}[/tex]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.
[tex]\begin{gathered} m=\frac{4}{3} \\ m_{\text{perpendicular}}=-\frac{1}{\frac{4}{3}} \\ m_{\text{perpendicular}}=-1\times\frac{3}{4} \\ m_{\text{perpendicular}}=-\frac{3}{4} \end{gathered}[/tex]Step 3: Get the y-intercept of the perpendicular line using the general equation of a line
[tex]\begin{gathered} y=mx+b \\ (x,y)=(-7,-2),m=-\frac{3}{4} \\ -2=-\frac{3}{4}(-7)+b \\ -2=\frac{21}{4}+b \\ b=-2-\frac{21}{4} \\ b=-\frac{8}{4}-\frac{21}{4} \\ b=\frac{-8-21}{4} \\ b=-\frac{29}{4} \end{gathered}[/tex]Step 4: We compute the final equation of the line perpendicular to y=4/3x+1 through point (-7,-2)
[tex]\begin{gathered} y=mx+b \\ y=-\frac{3}{4}x+(-\frac{29}{4}) \\ y=-\frac{3}{4}x-\frac{29}{4} \end{gathered}[/tex]Hence, the equation of the line perpendicular to y=4/3x+1 through point (-7,-2) is:
[tex]y=-\frac{3}{4}x-\frac{29}{4}[/tex]