Question

How do you find a standard form equation for the line with (-2,2) and is parallel to the line whose equation is 2x-3y-7=0?

Answer 1

`2x-3y+10=0`

Explanation:

`2x-3y-7=0` and any line parallel to it has a slope of `color(green)(m=2/3)`
`color(white)("XXX")`We know this either because:
`color(white)("XXX")[1]color(white)("XX")`we know `Ax+By+c=0` has a slope of `color(green)(-A/B)`
`color(white)("XXX")`or
`color(white)("XXX")[2]color(white)("XX")` by converting into slope-intercept form: `y=color(green)(m)x+b`
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If a line has a slope of `color(green)(2/3)` and passes through `(color(red)(-2),color(blue)(2))`
then it has a slope-point form of
`color(white)("XXX")y-color(blue)(2)=color(green)(2/3)(x-color(red)(""(-2)))`

Simplifying
`color(white)("XXX")y=color(green)(2/3)(x+2)+2`

`color(white)("XXX")3y=(2x+4) +6`

or (in standard form)
`color(white)("XXX")2x-3y+10=0`

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For verification/support, here are the graphs: