How do you write an equation of a line passing through (4, 2), perpendicular to #y=2x+3#?
See the entire solution process below:
Therefore, for this problem, the slope of the perpendicular line is:
Which means the equation is:
Substituting the slope we calculated and the values from the point in the problem gives:
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To write the equation of a line perpendicular to ( y = 2x + 3 ) passing through the point ( (4, 2) ), you need to determine the slope of the perpendicular line.
The slope of the given line ( y = 2x + 3 ) is 2.
Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the perpendicular line will be ( -\frac{1}{2} ).
Now that we have the slope ( -\frac{1}{2} ) and the point ( (4, 2) ), we can use the point-slope form of a linear equation:
[ y - y_1 = m(x - x_1) ]
Substitute the values:
[ y - 2 = -\frac{1}{2}(x - 4) ]
Now, expand and simplify:
[ y - 2 = -\frac{1}{2}x + 2 ]
[ y = -\frac{1}{2}x + 4 ]
So, the equation of the line passing through ( (4, 2) ) and perpendicular to ( y = 2x + 3 ) is ( y = -\frac{1}{2}x + 4 ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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