Line CD passes through point E.
Line CD: y−5=−3(x+2)
Point E: (6,−1)
What is the equation of the line that is perpendicular to line CD?
y=1/3x−4
y=−1/3x−19/3
y=−1/3x+5
y=−1/3x+19/3
y=1/3x+4
Answer i think is either the first one or last one
So you have the perpendicular slope correct : )
thus the equation looks like y = 1/3x + b ,
now sub in the point (6, -1) and solve for b : )
You said the line CD passes through point E
It does not.
To find the equation of a line that is perpendicular to line CD, we need to determine the slope of line CD and then find the negative reciprocal of that slope.
The given equation of line CD is in the slope-intercept form y = mx + b, where m is the slope of the line.
Line CD: y - 5 = -3(x + 2)
To write the equation in slope-intercept form, let's simplify it:
y - 5 = -3x - 6 (distribute -3)
y = -3x - 6 + 5 (add 5 to both sides)
y = -3x - 1
Comparing this equation to y = mx + b, we can see that the slope of line CD, m, is -3.
To find the negative reciprocal of -3, we flip the fraction and change its sign. Therefore, the negative reciprocal of -3 is 1/3.
Now we can write the equation of the line that is perpendicular to line CD:
Using the given point E(6, -1) and the slope 1/3, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the values, we have:
y - (-1) = 1/3(x - 6)
y + 1 = 1/3(x - 6)
y + 1 = 1/3x - 2
y = 1/3x - 2 - 1
y = 1/3x - 3
So, the equation of the line that is perpendicular to line CD is y = 1/3x - 3.
Therefore, the correct answer is the second option: y = 1/3x - 19/3.