Answer: [tex]y=\frac{1}{2}x+7[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of the line is the following:
[tex]y=mx+b[/tex]
Where m is the slope and b the y-intercept.
By definition, when two lines are perpendicular, their slopes are opposite reciprocals.
Then, to find the slope of the equation of the line given, you can solve for y:
[tex]4x+2y=6\\2y=-4x+6\\\\y=-2x+3[/tex]
As you can see, the slope of this line is -2.Then, the slope of the line that is perpendicular to it, must be:
[tex]m=\frac{1}{2}[/tex]
Substitute the slope and the point given, into the equation and solve for b:
[tex]8=\frac{1}{2}(2)+b\\8=1+b\\b=7[/tex]
Therefore, the equation of this line is:
[tex]y=\frac{1}{2}x+7[/tex]
