Write an equation of the line passing through point P(2, 3) that is perpendicular to the line y−4 = −2(x+3) .

Answer 1

y-4 = -2(x+3). We need to find the slope of this equation. Simplest way is to solve for y. (Put the equation in slope-intercept form.)

y-4 =-2x-6

y= -2x-2

Now we know the slope of the given line is -2. Slope of the perpendicular line is the inverse reciprocal of -2. (Change sign and flip.) m = 1/2

We are given that a point on this line is (2,3). We can find the equation in two different ways:

a) Plug in m, x, and y and solve for b in slope-intercept form:

3=(1/2)2 + b

3= 1+b

2=b

In slope-intercept form, the equation is: y=1/2x+2

b) Use point-slope form:

y-3 = 1/2(x-2)

y-3 = 1/2x-1

y = 1/2x+2

Answer 2

First we need to calculate the slope of the line y-4 = -2(x+3), which is in point-slope form.

y-y1 = m(x-x1).

Let's modify the equation to get it in the form y = mx + b, where m is the slope.

y-4 =-2(x+3)

y-4 = -2x -6

y = -2x -2

The slope of the line is -2. A line perpendicular to that line will have a slope of 1/2 (the negative inverse).

Given (2,3) is a point on the new line whose slope is 1/2, the equation of the new line in point-slope form would be:

(y-3) = 1/2(x-2)