Answer:
[tex]y=-2x+1[/tex]
Step-by-step explanation:
Given:
Equation of the line.
[tex]y = \frac{1}{2}x+1[/tex]
A point (-1, 3)
Solution:
Find the line [tex]y=mx+b[/tex] that perpendicular to the line y = \frac{1}{2}x+1 and passing through the point (-1, 3)
First we find the slope of the given line by comparing with [tex]y=mx+b[/tex]
So, slope of the line is [tex]m_{1}=\frac{1}{2}[/tex], and
We know that the slope of the perpendicular line is [tex]m_{1}\times m_{2}=-1[/tex]
So, the slope of the perpendicular line is.
[tex]m_{2}=-\frac{1}{m_{1}}[/tex]
Substitute [tex]m_{1}=\frac{1}{2}[/tex]
[tex]m_{2}=-\frac{1}{\frac{1}{2}}[/tex]
[tex]m_{2}=-2[/tex]
Now, we substitute point (x,y) = (-1, 3) and slope is equal to -2 in point slope formula for y-intercept of the line.
[tex]y=mx+b[/tex]
[tex]3=-2(-1)+b[/tex]
[tex]b = 3-2[/tex]
[tex]b=1[/tex]
So, the equation of perpendicular line with slope [tex]m_{2}=-2[/tex] and passing through the point (-1, 3)
[tex]y=-2x+1[/tex]
Therefore, line [tex]y=-2x+1[/tex] is perpendicular to the line y = \frac{1}{2}x+1 and passing through the point (-1, 3).
