Question

Give an equation of the line through the point (4, 1) and perpendicular to the line x + 5y = 1.

Answer 1

hmmm what do you think is the slope of => x + 5y = 1. ?

Answer 2

-1/5?

Answer 3

yeap is -1/5 so, the slope of a line perpendicular to that one, will be the NEGATIVE RECIPROCAL of that, that is \(\bf -\cfrac{1}{{\color{blue}{ 5}}}\qquad negative\to +\cfrac{1}{{\color{blue}{ 5}}}\qquad reciprocal\to +\cfrac{{\color{blue}{ 5}}}{1}\to 5\)

so you're really asked on how to find the equation of a line with slope of 5 and that passes through (4,1)
that is \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ 4}}\quad ,&{\color{blue}{ 1}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= 5
\\ \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

y-1=5(x-(-1)

Answer 5

y=5x+1?

Answer 6

\(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ 4}}\quad ,&{\color{blue}{ 1}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= 5
\\ \quad \\

y-{\color{blue}{ 1}}={\color{green}{ 5}}(x-{\color{red}{4}})\implies y-1=5x-20\implies y=5x-20+1\)

Answer 7

So that would be
y=5x-19?

Answer 8

yeap

Answer 9

thanks! but should it be in standard form?

Answer 10

well... it doesn't say above...so either will do I'd think, that's just the slope-intercept one, but you can put it in standard

Answer 11

Thanks! (-:

Answer 12

yw