Question

What is the equation of the line in slope–intercept form that passes through the point (0, 3) and is perpendicular to the line y = 2x – 6?

Answer 1

y = 2x + 6 has slope 2, therefore any line perpendicular to it will have slope -1/2 (the inverse reciprocal). The point (0,3) lies on the y-axis and is therefore the desired line's y-intercept. Since you need the equation in slope-intercept form, you've just got to throw the numbers into the equation.

y = mx + b
m = -1/2
b = 3

Therefore, DRUM ROLL PLEASE,
y = (-1/2)x + 3

Hope this helped!

Answer 2

the line whose eqn we need to find is perpendicular to line y = 2x – 6

slope of line y = 2x – 6 is
m=2

so slope of required line is negative inverse of given line i.e. -1/2

also the line passes through point (0,3)

eqn of line with given and a point is y-y1=m(x-x1)

where m=-1/2 and ( x1,y1)=(0,3)

plug in these values

y-y1=m(x-x1)
y-3=-1/2(x-0)

y-3=-x/2
y=(-x/2) + 3 is the required eqn of line