Respuesta :
Answer:
y=-[tex]\frac{1}{2}[/tex]x+[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
First, calculate the slope of the line that is perpendicular to the equation of line we are asked to find
m=(y2-y1)/(x2-x1)
=(2-(-4))/(-2-1)
=6/-3
=-2
in this equation the slope is 2, and to find the first equation, use y=mx+b
use the point (1, -4) to find b
-4=(2)(1)+b
-4=2+b
b=-6
the first equation of the line is y=2x-6
to find the x intercept of that line substitute 0 for y
0=2x-6
2x=6
x=3
the slope of a line perpendicular to this would be the opposite reciprocal of the slope which would be equal to -1/2
for the second equation of the line to pass thorugh the x-intercept of the first line, it must pass through (3, 0), so substitute and solve for b
y=mx+b
0=(-1/2)(3)+b
b=3/2
thus the equation of the line that is perpendicular to the line through (1,-4) and (-2, 2) and passes through the x intercept of that line is y=-[tex]\frac{1}{2}[/tex]x+3/2
The equation of the line that is perpendicular to the line through (1,-4) and (-2,2) is [tex]y= \frac{1}{2}x+3[/tex]
The equation of the line perpendicular to the line passing through the points (x₁, y₁) and (x₂, y₂) is given as:
[tex]y-y_1=\frac{-1}{m} (x-x_1)[/tex]
The slope m is calculated using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{2-(-4)}{-2-1} \\\\m=\frac{6}{-3} \\\\m=-2[/tex]
For the line passing through the points (1,-4) and (-2,2), substitute m = -2, x₁ = 1, and y₁ = -4 into the equation [tex]y-y_1=\frac{-1}{m} (x-x_1)[/tex]
[tex]y-1=\frac{-1}{-2} (x-(-4))\\\\y-1=\frac{1}{2}(x+4)\\\\y=\frac{1}{2}x+2+1\\\\y= \frac{1}{2}x+3[/tex]
Learn more on equation of a line here: https://brainly.com/question/13763238
