Answer: [tex]y=x-6[/tex]
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
By definition, the slopes of perpendicular lines are negative reciprocals.
Given the line:
[tex]y=-x[/tex]
We know that a line perpendicular to this line must have this slope:
[tex]m=\frac{1}{1}=1[/tex]
Since that line goes through the point (8,2), we can substitute the slope 1 and these coordinates into [tex]y=mx+b[/tex] and solve for "b":
[tex]2=(1)(8)+b\\\\2-8=b\\\\b=-6[/tex]
Therefore, the equation of this line is:
[tex]y=x-6[/tex]
