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.
