Question

What is the equation of the line in slope-intercept form? the line perpendicular to

y = 1/3x + 5 through (2, 1)

A. y = 1/3x + 7

B. y = -3x + 7

C. y = 3x + 7

D. y = -1/3x + 7

Answer 1

Perpendicular lines have inverse reciprocal slopes, i.e. two perpendicular lines A, B have slopes related by \(m_a=-\frac1{m_b}\). As our original line has slope \(\frac13\), our perpendicular line must have slope \(-\frac1{\frac13}=-1\times\frac31=-3\). Now that we have our new line's slope, we can use *point-slope form* \(y-y_1=m(x-x_1)\) to derive an equation for the line.$$y-1=-3(x-2)\\y-1=-3x+6$$Our last step is to put this in slope-intercept form, which should just take a little algebraic manipulation (add \(1\) to both sides):$$y=-3x+7$$

Answer 2

thank you!!! :)