Question

write an equation of a line perpendicular to y=1/4x+4 in slope intercept form that passes through the point (-2,6).

a) y=1/4x -4
b)y=1/4x +6
c) y=-4x -2
d) y=-4x +1/4

Answer 1

hmm what's the slope of -> y=1/4x+4 anyway?

Answer 2

1/4?

Answer 3

yeap... so we know the slope of this equation is 1/4

so the equation of a line that is PERPENDICULAR to this one will be the NEGATIVE RECIPROCAL of that, that is \(\bf \cfrac{1}{{\color{blue}{ 4}}}\qquad negative\to - \cfrac{1}{{\color{blue}{ 4}}}\qquad reciprocal\to - \cfrac{{\color{blue}{ 4}}}{1}\to {\color{blue}{ 4}}\)

so you're really asked on "what is the equation of a line with slope of "4" and that passes through (-2,6)"

so \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 6}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= 4
\\ \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} \)

Answer 4

well... actually shold be MINUS 4 ahemm so \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 6}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= -4
\\ \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} \)

Answer 5

\(\bf \bf \cfrac{1}{{\color{blue}{ 4}}}\qquad negative\to - \cfrac{1}{{\color{blue}{ 4}}}\qquad reciprocal\to - \cfrac{{\color{blue}{ 4}}}{1}\to {\color{blue}{ -4}}\)

Answer 6

ok so im going to plug this in

Answer 7

yeap and then you can just solve for "y" if you need it in "slope-intercept" form

Answer 8

which of the answers would it be can you solve it please so i dont get it wrong?

Answer 9

because im getting a little confused

Answer 10

well... what have you gotten so far?

Answer 11

y-6=1/4(x-(-2)

Answer 12

\(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 6}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= -4
\\ \quad \\

y-{\color{blue}{ 6}}={\color{green}{ -4}}(x-{\color{red}{ (-2)}})\implies y-6=-4(x+2)\implies y-6=-4x-8
\\ \quad \\
y=-4x-8+6\implies y=-4x-2\)

Answer 13

yay!!! thank you soooo much

Answer 14

yw