y-3=3(x+1) what is the x-intercept of this line? & what is the equation in standard form of a line parallel to the given line that passes through (o,-2)?

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At the x intercept y=0. So,

`0-3=3(x+1)`

`rArr -3=3x+3`

`rArr 3x=-6`

`rArr x=-2`

Hence, the x intercept of the line is -2.

2) The given line is y-3=3(x+1)

Expressing it in the slope intercept form gives:

y=3x+6

Hence, its slope,m=3.

The point slope form of the parallel line is:

`y-y_1=m(x-x_1)`

Here, `(x_1,y_1)=(0,-2)` and` m=3.`

Plugging in the values we get:

`y-(-2)=3(x-0)`

`rArr y+2=3x`

`rArr 3x-y=2`

Therefore, the equation of the parallel line in the standard form is:

3x-y=2.

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