The missing figure of the given line is attached
The equation in the point-slope form of the line is [tex]y+3=\frac{1}{4}(x+4)[/tex] ⇒ 3rd answer
Step-by-step explanation:
The relation between the perpendicular lines
- The product of their slopes is -1
- If 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 line
From the attached figure
The 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
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