Answer:
[tex]y=2x+7[/tex]
Step-by-step explanation:
The correct question is
what is the equation for a line passing through (-2,3) and perpendicular to y= -1/2x+1 ?
Remember
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes are equal to -1)
The slope of the given line is m=-1/2
so
the opposite reciprocal is m=2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=2\\point\ (-2,3)[/tex]
substitute
[tex]y-3=2(x+2)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
isolate the variable y
[tex]y-3=2x+4[/tex]
[tex]y=2x+4+3[/tex]
[tex]y=2x+7[/tex]
