equation of the line perpendicular to y=1/4x=10 through (5,7) write answer in standard form

Question

Help I am so stuck on this problem

Answer 1

Perpendicular lines means negative reciprocal slopes.

So you know the slope, m2, of line2, if line 1 is y=1/4x-10 (I think that there was a typo here at the second equals sign), with a slope of 1/4, m1, is m2 = -4.

These slopes can be understood by looking at the lines in slope intercept, y=mx+b, form where m is the slope and b is the y coordinate of the point where the line crosses the y axis.

So our desired perpendicular line, line2, can be written as y = m2*x + b, or y = -4x + b. But we are also given that line2 passes through the point (5,7), so we can put 7 and 5 into our equation, for y and x respectively, and figure out what b is an voila! We have line2.

Answer 2

Hi Maureen N.,

Maybe part of the problem is that you copied the question wrong. Did you mean y = (1/4)x - 10 , or perhaps y = (1/4)x + 10 ? It has to be one or the other: y = (1/4)x = 10 is a point, not a line! So therefore, it's useless to speak of a perpendicular to it.

Once you get the right form, then use the fact that a perpendicular to a line with slope a has slope (-1/a). So write a general equation for that line, then solve for the unknown constant (the y-intercept) by substituting your known point coordinates in.

-- Cheers, -- Mr. d.