What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, −3)?y + 3 = −4(x + 4)y + 3 = –One-fourth(x + 4)y + 3 = One-fourth(x + 4)y + 3 = 4(x + 4)

The missing figure of the given line is attachedThe equation in the point-slope form of the line is  [tex]y+3=\frac{1}{4}(x+4)[/tex] ⇒ 3rd answerStep-by-step explanation:The relation between the perpendicular linesThe product of their slopes is -1If the slope of one of them is m, then the slope of the other is [tex]\frac{-1}{m}[/tex]The formula of the slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]The point-slope form of the equation of a line is [tex]y-y_{1}=m(x-x_{1})[/tex] , where [tex](x_{1},y_{1})[/tex] is a point on the lineFrom the attached figureThe given line passes through points (-1 , 1) and (0 , -3), use them to find the slope of the line∵ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = 0∵ [tex]y_{1}[/tex] = 1 and [tex]y_{2}[/tex] = -3∴ The slope of the given point = [tex]\frac{-3-1}{0-(-1)}=\frac{-4}{1}=-4[/tex]∵ The product of the slopes of the perpendicular lines is -1∵ The slope of the given line = -4- Reciprocal the number and change its sign∴ The slope of the perpendicular line = [tex]\frac{1}{4}[/tex]∵ The slope-form of the equation is [tex]y-y_{1}=m(x-x_{1})[/tex]∵ [tex]m=\frac{1}{4}[/tex]∵ The line passes through point (-4 , -3)∴ [tex]x_{1}[/tex] = -4 and [tex]y_{1}[/tex] = -3- Substitute these values in the form of the equation∴ [tex]y-(-3)=\frac{1}{4}(x-(-4))[/tex]∴ [tex]y+3=\frac{1}{4}(x+4)[/tex]The equation in the point-slope form of the line is [tex]y+3=\frac{1}{4}(x+4)[/tex]Learn more:You can learn more about the equation of the perpendicular line in brainly.com/question/11223427#LearnwithBrainly