Question

Which of the following equations defines a line that is parallel to the line begin equation . . . y equals . . . begin fraction . . . negative 4 over 3 . . . end fraction, times x . . . minus 4 . . . end equation and passes through the point begin ordered pair . . . 3 . . . comma . . . negative 1 . . . end ordered pair?

A
begin equation . . . y equals . . . begin fraction . . . negative 4 over 3 . . . end fraction, times x . . . minus 1 . . . end equation

B
begin equation . . . y equals . . . begin fraction . . . negative 4 over 3 . . . end fraction, times x . . . minus 3 . . . end equation

C
begin equation . . . y equals . . . begin fraction . . . negative 4 over 3 . . . end fraction, times x . . . plus 1 . . . end equation

D
begin equation . . . y equals . . . begin fraction . . . negative 4 over 3 . . . end fraction, times x . . . plus 3 . . . end equation

Answer 1

Answer:

Option D

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

Step-by-step explanation:

step 1

we have

$y=-\frac{4}{3}x-4$ ----> given line

we know that

If two lines are parallel, then their slopes are equal

so

The slope of the given line is

$m=-\frac{4}{3}$

That means

The slope of the line parallel to the given line is also

$m=-\frac{4}{3}$

step 2

Find the equation of the line in slope intercept form

$y=mx+b$

where

m is the slope

b is the y-intercept

we have

$m=-\frac{4}{3}$

$point\ (3,-1)$

substitute in the linear equation and solve for b

$-1=-\frac{4}{3}(3)+b$

$-1=-4+b\\b=3$

The linear equation is

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

therefore

begin equation . . . y equals . . . begin fraction . . . negative 4 over 3 . . . end fraction, times x . . . plus 3 . . . end equation