Question

1. Find the equation of a line that passes through the point (4,1) and is perpendicular to the

line that contains the points (3,-7) and (-1,9).

Answer 1

x - 4y = 0 . . . in standard form

y = (1/4)x . . . in slope-intercept form

Explanation:

The slope of the given line is ...

m = (y2 -y1)/(x2 -x1) = (9 -(-7))/(-1 -3) = 16/-4 = -4

The slope of the perpendicular line is the negative reciprocal of this:

desired slope = -1/m = -1/-4 = 1/4

This can be used in the point-slope form of the equation of a line:

y -h = m(x -k) . . . . . line with slope m through point (h, k)

Your perpendicular line has a slope of 1/4 and goes through point (4, 1), so its equation can be written as ...

y -1 = (1/4)(x -4)

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

y = (1/4)x

In standard form, this is ...

4y = x

x -4y = 0