Question

Question #d842e

Answer 1

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

Or converting to the slope-intercept form:

`y = 2/3x - 3`

Explanation:

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

`2x-3y=9`

Explanation:

`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`