Answer: [tex]y- 3 =-2(x + 4)[/tex]
Step-by-step explanation:
The equation of a line passing through [tex](x_1,y_1)[/tex] in point slope form is given by ;-
[tex](y-y_1)=m(x-x_1)[/tex], where m is the slope of the line .
The slope of the line passing from (a,b) and (c,d) is given by :-
[tex]m=\dfrac{d-b}{c-a}[/tex]
Then the slope of the line passing from (-4, -3) and (4, 1) is given by :-
[tex]m=\dfrac{1-(-3)}{4-(-4)}=\dfrac{1+3}{4+4}=\dfrac{4}{8}=\dfrac{1}{2}[/tex]
The slope of perpendicular line = [tex]m_1=\dfrac{-1}{m}=\dfrac{-1}{\dfrac{1}{2}}=-2[/tex] [∵ product of slopes of two perpendicular line is -1]
Hence, the the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, 3) will be
[tex]y- 3 =-2(x + 4)[/tex]
