Write an equation of a line that is perpendicular to y = 3x + 3 and passes through (−6, 3).
A. y equals negative one-third times x plus 1
B. y equals negative one-third times x minus 5
C. y = 3x + 21
D. y = 3x − 15
slope of y = 3x + 3 is 3, so the slope of your perpendicular is -1/3
using the given point (-6,3)
y - 3 = (-1/3)(x + 6)
times 3
3y - 9 = -x - 6
x + 3y = 3
or, if you insist ..
3y = -x + 3
y = (-1/3)x + 1
To find an equation of a line that is perpendicular to another line, we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
The given line has a slope of 3, so the perpendicular line will have a slope of -1/3.
Using the point-slope form of a line equation, we can plug in the slope (-1/3) and the given point (-6, 3) to find the equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Plugging in the values, we get:
y - 3 = (-1/3)(x - (-6))
y - 3 = (-1/3)(x + 6)
Multiplying through by -3 to eliminate the fraction, we get:
-3(y - 3) = x + 6
-3y + 9 = x + 6
Rearranging the equation in the form y = mx + b, we have:
-3y = x + 6 - 9
-3y = x - 3
Dividing through by -3, we get:
y = (-1/3)x + 1
Therefore, the equation of a line that is perpendicular to y = 3x + 3 and passes through (-6, 3) is:
y = (-1/3)x + 1
So, the correct answer is option A.
To find an equation of a line that is perpendicular to the given line, we need to determine the negative reciprocal of the slope of the given line.
The given line has a slope of 3. The negative reciprocal of 3 is -1/3.
Using point-slope form, we can write the equation of the perpendicular line as:
y - y1 = m(x - x1),
where (x1, y1) is the given point (-6, 3), and m is the negative reciprocal of the slope.
Plugging in the values, we have:
y - 3 = (-1/3)(x - (-6)),
y - 3 = (-1/3)(x + 6),
y - 3 = (-1/3)x - 2,
y = (-1/3)x + 1.
Therefore, the equation of the line that is perpendicular to y = 3x + 3 and passes through (-6, 3) is y = (-1/3)x + 1.
Hence, the correct answer is option A: y equals negative one-third times x plus 1.