find the equation of a straight line which passes through the point (-3,5) and is perpendicular to the line 2x - 3y + 1 =0 and 4y+3x+2 =0
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Question: What is the equation of the straight line passing through the point (3,5) which is perpendicular to the line y=3x+2?
The slopes of perpendicular lines are negative reciprocals of each other. The slope of the given line is the slope of the perpendicular line is
Starting writing the equation of the line
where b is the y-intercept, plug in the coordinates of the given point
solve for b
The equation of the requested line is:
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James Wright
, BS Physics & Mathematics, University of Illinois at Chicago (1972)
Answered May 26, 2021 · Author has 948 answers and 311.4K answer views
If this line is perpendicular to the line y(1) = 3x + 2, then its slope must be the inverse negative of the reference line y(1). In the general line equation y = mx + b, m is the slope of the line. In the case of y(1), m = 3, so the line we’re looking for, y(2), must have a slope of -1/3. The general equation of all lines with this slope is:
y(unk) = (-1/3)x + b
But I still have an unknown term, b, to figure out.
I am told that this unknown line y(2) passes through the point (3,5), so the above equation must be true for (3,5). In order to find b, I only need substitute (3,5) for x and y in y(unk) and get the following: 5 = (-1/3)3 + b or 5 = -1 + b which reduces to b = 6. So the line I’m searching for is y(2) = (-1/3)x + 6