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

x + 2y + 4 =0

Explanation:

1) You know a point (4 - 1) and that the line is perpendicular to a given line.

2) From the equation of the perpendicular line whose equation was given, you determine the slope, for which you can use the slope-intercept form of the equation: 

2x - y - 7 = 0 => y = 2x + 7.

The slope is the coeffiicient of x, which is 2.

Therefore, slope = 2.

3) The slope of the other line is the negative inverse of the slope of the perpedicular line:

slope = - 1/2

4)  Now that you have the slope of your line and the point (4, - 1) you determine the equation with this procedure:

y - b
= slope
x - a

where a y b are the coordinates of the point (4, - 1) and the slope is -1/2

=>

 y - (-1)
= - 1/2
  x - 4

5) Simplify

2(y + 1) = - (x - 4)

2y + 1 = - x + 4

2y + x +1 + 4 = 0

x + 2y + 4 =0 < this is the equation searched.