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18.02.2020 •
Mathematics
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
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Ответ:
Option D
Step-by-step explanation:
step 1
we have
we know that
If two lines are parallel, then their slopes are equal
so
The slope of the given line is
That means
The slope of the line parallel to the given line is also
step 2
Find the equation of the line in slope intercept form
where
m is the slope
b is the y-intercept
we have
substitute in the linear equation and solve for b
The linear equation is
therefore
begin equation . . . y equals . . . begin fraction . . . negative 4 over 3 . . . end fraction, times x . . . plus 3 . . . end equation
Ответ: