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 +
B. y = -3x + 7
C. y = -1/3x + 7
D. y = 3x + 7

Answer 1

@cormacpayne ?:)

Answer 2

what's the slope of --> y = 1/3x + 5 anyway ?

Answer 3

Idk i learned this along time ago i just totally forgot how to do it /.\

Answer 4

ok.. well \(\bf y={\color{brown}{ \cfrac{1}{3}}}x+5\qquad {\color{brown}{ slope}}\)

see the slope of that one now?

Answer 5

1/3x right?

Answer 6

yeap

so the slope of a line perpendicular to that one, will be NEGATIVE RECIPROCAL of that

meaning \(\bf \cfrac{1}{{\color{blue}{ 3}}}\qquad reciprocal\to \cfrac{{\color{blue}{ 3}}}{1}\qquad negative\to -\cfrac{{\color{blue}{ 3}}}{1}\)

Answer 7

or just -3 for short

Answer 8

Oh okay thanks :)

Answer 9

so you're really being asked,
"what is the equation of a line that passes through (2,1) and has a slope of -3 ?"

so \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ 2}}\quad ,&{\color{blue}{ 1}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= -3
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)