Write the equation of a line that passes through the point ( - 6, 4) and is perpendicular to the line y = -2x+1

Question

Write the equation of a line that passes through the point ( - 6, 4) and is perpendicular to the line

y = -2x+1

Answer 1

The most important thing to remember about perpendicular slopes is that they are negative reciprocals of each other. So they are opposite sign and if one is m, the other is -1/m.

You can use the point-slope form of a line y-y1 = m(x-x1) to get the equation of the second line.

y-4 = (1/2)(x+6) and then you could algebra to convert to slope intercept form if asked for it.

Answer 2

We start from general equation of a line.

y = m x + b

If this line is perpendicular to y = -2 x +1 , its slope must be negative and reciprocal of this line. The slope of the given line is -2 (the coefficient of x) . The slope of our line is.

m = - 1 / (-2) = 1/2 = 0.5

So our general equation is now.

y = 0.5 x + b

To find b. we must use the point (-6,4) , if the line passes through this point , this point should work in the equation. it means x = -6 and y = 4 so

y = 0.5 x + b

4 = 0.5 ( -6 ) + b

4 = -3 + b

7 = b

b = 7

So the final answer is

y = 0.5 x + 7