Question

What is the equation of the line described below written in slope-intercept form?

the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0
y=-3x+1
y= 2x-1
y=2x + 1

Answer 1

y= -1/2 x+1

Explanation:

2x-y-7=0

2x-7=y

y=2x-7

Answer 2

y = - (1/2) x + 1

Explanation:

The given equation of the line is:

2 x - y - 7 = 0

solving for y gives:

2 x - 7 = y

so y = 2 x - 7

where the slope is "2", which is fundamental to know in order to construct a perpendicular line to it by using the "opposite of the reciprocal" of the given slope.

So in our case, the slope of the perpendicular line must be: "- 1 / 2" (negative one half).

now we can build the equation of the new line, using this slope and requesting the point (4, -1) to be in it:

y = - (1/2) x + b

-1 = - (1/2) (4) + b

-1 = - 2 + b

solve for b:

b = 2 - 1 = 1

Then the equation of the perpendicular line is:

y = - (1/2) x + 1