Question

find the equation of a line parallel to the line 3x-4y+2=0 and passing through the point (-2,3)​

Answer 1

Answer:

$y=-\frac{3}{4} x+\frac{3}{2}$

Step-by-step explanation:

if a line is parallel to a line they both have the same gradient

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Start by finding the gradient of: 3x+4y+2=0

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$3x+4y+2=0\\\\\\(3x+4y+2)-2=(0)-2\\\\\\3x+4y=-2\\\\\\(3x+4y)-3x=(-2)-3x\\\\\\4y=-2-3x\\\\\\\\\frac{(4y)}{4} =\frac{(-2-3x)}{4} \\\\\\y=\frac{-2-3x}{4} \\\\\\y=\frac{-2}{4} - \frac{3x}{4\\}\\\\\\y=-\frac{1}{2} -\frac{3}{4}x \\\\\\y=-\frac{3}{4}x -\frac{1}{2}$

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so $-\frac{3}{4}$ is the gradient m

y=mx+c

y=-3x+c

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c is the y intercept

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if y=mx+c,

  c=y-mx

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(-2,3) are coordinates where (-2) is x and (3) is y

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substitute:

$c=y-mx\\c=3-(-\frac{3}{4} *-2 )\\c=3-(\frac{3}{2} )\\c=\frac{3}{2}$

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The equation of a line is ( y = mx+c )

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substitute:

$y=mx+c\\\\y=-\frac{3}{4} x+\frac{3}{2}$

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Hope it helped..