Question

write the equation of the line that is parallel to the line 2x+3y=5 and contains the point (-2 1)

Answer 1

hmmm if you solve "2x+3y=5" for "y"..... what would it look like?

Answer 2

basically what jdoe is saying, is in y = mx + b form, the slope is in the m position. So solve for y is the same thing

Answer 3

y=-2x/3+5/3?

Answer 4

2x + 3y = 5
3y = -2x + 5
y = -2/3x + 5/3

y = mx + b ....slope is in the m position
so what is the slope ?

Answer 5

-2/3

Answer 6

so the slope of a line parallel to that one, will have the same slope as that one... thus \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 1}})
\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 7

correct....and a parallel line will have the same slope.

so now use y = mx + b again
slope(m) = -2/3
(-2,1).....x = -2 and y = 1
we already know the slope(m), but we need to find the y intercept(b)
so we sub
y = mx + b
1 = -2/3(-2) + b
1 = 4/3 + b
1 - 4/3 = b
3/3 - 4/3 = b
-1/3 = b

so your equation in slope intercept form is : y = -2/3x - 1/3

do you have any questions ?

Answer 8

well..... you're not asked to put it in slope-intercept form, so.... I gather you don't have to solve it for "y"

Answer 9

no questions

Answer 10

good to hear :)....just remember, that a parallel line will have the same slopes, but perpendicular lines are another story

Answer 11

thanks to both :P