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Answer 1 · 2017-01-24T17:31:44

$(y + color(red)(1)) = color(blue)(2/3)(x - color(red)(3))$

Or converting to the slope-intercept form:

$y = 2/3x - 3$

First, we need to find the slope of the equation given in the problem by converting it to the familiar slope-intercept form by solving for $y$ :

$2x - color(red)(2x) - 3y = -color(red)(2x) + 8$

$0 - 3y = -2x + 8$

$-3y = -2x + 8$

$(-3y)/color(red)(-3) = (-2x + 8)/color(red)(-3)$

$(color(red)(cancel(color(black)(-3)))y)/cancel(color(red)(-3)) = 2/3x - 8/3$

$y = 2/3x - 8/3$

The slope-intercept form of a linear equation is:

$y = color(red)(m)x + color(blue)(b)$

Where $color(red)(m)$ is the slope and $color(blue)(b)$ is the y-intercept value.

Therefore we know the slope of this line and a line parallel to this line is $color(red)(m = 2/3)$

We can now use this slope and the point and the point-slope formula to find an equation for the line requested in the problem:

The point-slope formula states: $(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))$

Where $color(blue)(m)$ is the slope and $color(red)(((x_1, y_1)))$ is a point the line passes through.

Substituting the values from the problem and the calculate gives:

$(y - color(red)(-1)) = color(blue)(2/3)(x - color(red)(3))$

$(y + color(red)(1)) = color(blue)(2/3)(x - color(red)(3))$

Or converting to the slope-intercept form:

$y + color(red)(1) = 2/3x - (2/3 xx color(red)(3))$

$y + 1 = 2/3x - 2$

$y + 1 - 1 = 2/3x - 2 - 1$

$y = 2/3x - 3$

Answer 2 · 2017-01-24T17:34:04

$2x-3y=9$

$2x-3y=8$
we change to $y=mx+c$ , where $m$ =gradient.

$2x-8=3y$
$y=(2x-8)/3$
$y=2/3x-8/3$

since it is a parallel line, they have a same value of gradient,where $m=2/3$ .

use $y-y_1=m(x-x_1)$
$y-(-1)=2/3(x-3)$
$y+1=2/3x-2$
$y=2/3x-2-1$
$y=2/3x-3$
$3y=2x-9$
$9=2x-3y$