which is the equation for the line perpendicular to y=-5/3x+11 1/3 and containing P(-2,3)?
A. y-2=-3/5(x-3)
B. y=-5/3x+4 1/3
C. y=-3/5x+4 1/5
D. y=3/5x+4 1/5
I think it may be D, is this right?
C
D
A
A
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1. -3/4, 4/3
2.y=3/5x+4 1/5
3. parallel
4. product of their slope is -1
To find the equation of the line perpendicular to y = -5/3x + 11 1/3 and passing through the point P(-2,3), we need to determine the slope of the perpendicular line.
First, we can observe that the given equation is in the form y = mx + b, where m is the slope of the line. In this case, the slope of the given line is -5/3.
For any line that is perpendicular to another line, the slopes are negative reciprocals of each other. This means that the slope of the perpendicular line will be the negative reciprocal of the slope -5/3, which is 3/5.
Now, we have the slope of the perpendicular line (3/5) and a point that lies on that line (-2,3).
Using the point-slope form of a linear equation y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values:
y - 3 = 3/5(x - (-2))
y - 3 = 3/5(x + 2)
y - 3 = 3/5x + 6/5
To put the equation in the slope-intercept form y = mx + b, we can add 3 to both sides:
y = 3/5x + 6/5 + 3
y = 3/5x + 6/5 + 15/5
y = 3/5x + 21/5
Comparing this equation to the possible answer choices, we see that the equation matches option D: y = 3/5x + 4 1/5.
Therefore, the correct answer is D.