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Find the equation of the line through point (-2, -2) and parallel to 3x + 4y =12

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Answer:

3x + 4y = - 14

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

3x + 4y = 12 ( subtract 3x from both sides )

4y = - 3x + 12 ( divide all terms by 4 )

y = -  x + 3 ← in slope- intercept form

with slope m = -

Parallel lines have equal slopes, thus

y = -  x + c ← is the partial equation

To find c substitute (- 2, - 2) into the partial equation

- 2 =  + c ⇒ c = -

y = -  x -  ← in slope- intercept form

Multiply through by 4 to clear the fractions

4y = - 3x - 14 ( add 3x to both sides )

3x + 4y = - 14 ← in standard form

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Answer:

3x + 4y = - 14

Step-by-step explanation:

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