Question

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

Answer 1

Answer:

  x - 4y = 0 . . . in standard form

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

Step-by-step 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