Question

What is the equation of the line parallel to the graph of `4x+3y=9` that passes through the point `(2, -1)`?

Answer 1

`y_1=(-4/3)x+5/3`

Explanation:

Two straight lines are parallel if and only if they have same slope.
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Name the new straight line parallel to the given straight line is
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`y_1=a_1x+b_1`
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`4x+3y=9`
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`rArr3y=-4x+9`
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`rArry=(-4/3)x+9/3`
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`rArry=(-4/3)x+3`
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The slope in the given straight line is `-4/3` then the `a_1=-4/3`
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Since the straight line`" "color(blue)(y_1)" "`passes through the
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point `(2,-1)` we can easily find `color(blue)(b_1)`
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`-1=-4/3(2)+b_1`
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`rArr-1=-8/3+b_1`
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`rArrb_1=-1+8/3`
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`rArrb_1=+5/3`
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Therefore, the equation of the straight line is :
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`y_1=(-4/3)x+5/3`