Find the equation of the line passing through the point (–1, 5) and perpendicular to the line y = – 3x + 4.
Question 6 options:
A)
3y = –x + 16
B)
y = –3x + 2
C)
3y = x + 16
D)
y = –3x + 8
To find the equation of the line perpendicular to y = -3x + 4, we need to determine the slope of the perpendicular line. The slope of the given line is -3, so the slope of the perpendicular line is the negative reciprocal of -3, which is 1/3.
Now, we have the slope of the perpendicular line and a point that it passes through (-1, 5). We can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we get:
y - 5 = (1/3)(x - (-1))
Simplifying, we get:
y - 5 = (1/3)(x + 1)
Multiplying both sides by 3 to eliminate the fraction, we get:
3y - 15 = x + 1
Rearranging the equation to have the variables on one side, we get:
x - 3y = -16
Therefore, the equation of the line passing through (-1, 5) and perpendicular to y = -3x + 4 is:
x - 3y = -16
So, the correct choice is option C) 3y = x + 16.
To find the equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line is y = -3x + 4. The slope of this line is -3.
The negative reciprocal of -3 is 1/3.
Now, we have the slope (m) and the given point (-1, 5). We can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values, we get:
y - 5 = (1/3)(x - (-1))
y - 5 = (1/3)(x + 1)
Now, simplifying the equation, we have:
y - 5 = (1/3)x + 1/3
Adding 5 to both sides, we get:
y = (1/3)x + 16/3
Multiplying both sides by 3 to eliminate the fraction, we get:
3y = x + 16
Therefore, the equation of the line passing through the point (-1, 5) and perpendicular to the line y = -3x + 4 is option A) 3y = x + 16.