Question

Write the equation of the line that goes through the point (-1, 4) and is perpendicular to the line 2x + 3y – 8 = 0 in general form.

Answer 1

what's the slope of => 2x + 3y – 8 = 0 ?

Answer 2

well, solve the equation first for "y"
see what you get

Answer 3

y = (-2/3)x + (8/3) this should be the answer for Y
x = 4

Answer 4

well, no quite yet

that's just to get the slope for that equation

\(\begin{matrix}
y=&\color{red}{-\cfrac{2}{3}}x&+\cfrac{8}{3}\\
& \color{red}{slope}&
\end{matrix}\)

Answer 5

so the slope of that equation is -2/3

the slope for a PERPENDICULAR line to that one, will be NEGATIVE RECIPROCAL of that one
what does that mean?

this one is -2/3
RECIPROCAL of that
-3/2
NEGATIVIZE it
3/2

Answer 6

So that would be the answer? Or just the slope?

Answer 7

so now we know that, the other line has a slope of 3/2 and goes through the point (-1, 4)

so we use that and plug it in the point-slope form of \(\bf y-y_1=m(x-x_1)\)
\(\bf (x_1, y_1) \implies (-1, 4)\)

Answer 8

m = slope

Answer 9

M= 3/2

Answer 10

\(\bf m = slope = \cfrac{3}{2}\\
(x_1, y_1) = (-1,4)\\
\color{blue}{y-y_1=m(x-x_1)}\implies y-(4)=\cfrac{3}{2}(x-(-1))\)

then again, just solve for "y", to get the equation :)

Answer 11

Y - (4) = 3/2 (x -(-1))?
and find the value of Y?

Answer 12

yes, so-called finding or solving for "y", is really just going to make it in y = ax+b form
which is the so-called slope-intercept form of the equation, which I think it's what's expected

Answer 13

How do i find Y?

Answer 14

\(\bf y-(4)=\cfrac{3}{2}(x-(-1)) \implies y-4 = \cfrac{3(x+1)}{2}\\
2y-8 = 3(x+1) \implies \square? = \square?\)

Answer 15

\(\bf 2y-8 = 3(x+1) \implies 2y-8 = 3x+3 \implies \square? = \square?\)