Question

Write an equation for a line through P. That is parallel to line L. Write another equation for a line through P that is perpendicular to line L.
P(2,4)
L: 2x+3y=4

Answer 1

Please help! I know I need to find slope and plug it in, but I am lost...

Answer 2

hmmm so.. can you solve "2x+3y=4" for "y"? what would that give you?

Answer 3

Y=-2/3 +4/3

Answer 4

yeap... any ideas on what the slope might be?

Answer 5

Sorry -2/3x+4/3

Answer 6

-2/3

Answer 7

well... so a line parallel to that one, will have the same slope of -2/3
and we also know it passes through P(2,4)

so \(\bf \begin{array}{lllll}
&x_1&y_1\\
P&({\color{red}{ 2}}\quad ,&{\color{blue}{ 4}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= -\cfrac{2}{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} \)

Answer 8

and you'd do, more or less the same for the perpendicular one, with the exception that
a perpendicular has a NEGATIVE RECIPROCAL slope to that one, thus \(\bf -\cfrac{2}{{\color{purple}{ 3}}}\qquad negative\to +\cfrac{2}{{\color{purple}{ 3}}}\qquad reciprocal\to \cfrac{{\color{purple}{ 3}}}{2}\)

so for the reciprocal we know the slope is 3/2 and passes through P(2,4) thus \(\bf \begin{array}{lllll}
&x_1&y_1\\
P&({\color{red}{ 2}}\quad ,&{\color{blue}{ 4}})\quad
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{3}{2}
\\ \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 9

3/2(x-2) +4

Answer 10

for the perpendicular, yes

I gather you don't have to solve for "y", unless you need it in slope-intercept form.... which seems you don't have to

Answer 11

What would the simplified version look like?
3/2x+4?

Answer 12

@jdoe0001 can you help me finish this problem really quickly! I'm sorry for keeping you busy

Answer 13

ok \(\bf y-4=\cfrac{3}{2}(x-2)\implies y-4=\cfrac{3}{2}x-3\implies y=\cfrac{3}{2}x+1\)

Answer 14

Thanks a ton!,

Answer 15

yw