Which is the equation of a line that is parallel to -3x + 4y = 4 and passes through the point (4,0)?

Question

A. y = 4/3x + 3

B. y = −3/4x −3

C. y = 4x + 3

D. y = 3/4x − 3

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Answer 1 · 2017-01-15T04:52:51

D. $y = 3/4x - 3$

Parallel lines have the same slope.
Transform the given equation to slope-intercept form

$-3x + 4y = 4$

$=> 4y = 3x + 4$

$=> y = 3/4x + 1$

$=> m = 3/4$

The parallel line has the equation

$y = 3/4x + b$

Use the point that the line passes through to determine the y-intercept

$0 = 3/4(4) + b$

$-3 = b$

Hence, the equation of the line is

$y = 3/4x -3$