Please help me

Question

find an equation of the line is perpendicular to y=1/2  X+ 11 and passed through (2,-6) 

y? X?

Answer 1

HI Star.

 

The slope of the line given (y=1/2 x + 11) is 1/2

 

The slope of a line perpendicular to it had a slope that is the "negative reciprocal".  Big words for take the current slope and flip it and change the sign.   

 

The slope of the line perpendicular is  -2/1 or just -2.

 

Once you know the slope (-2) and a point (2, -6), you can write the equation.

 

Know that y=mx+b

Know that m=-2

Know that when x=2, y=-6 (from the point given (2, -6))

 

Put all of this into y=mx+b, and solve for "b"

 

-6 = (-2)(2)+b

 

Simplify the right side:   -6 = -4 + b

 

Add 4 to both sides:   -2 = b

 

Now you know the "b" in y=mx+b, and you can write the equation:  y = -2 x -2

 

Final answer:  y = -2x - 2