two perpendicular lines intersect at the point (2,3). One line has a y-intercept of (0,5). Which of the following is the equatio
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Equation of a line is .
A perpendicular bisector is a line that cuts a line segment connecting two points exactly in half at a 90 degree angle. To find the perpendicular bisector of two points, all you need to do is find their midpoint and negative reciprocal, and plug these answers into the equation for a line in slope-intercept form.
Given that,
Endpoints of the line segment are () = (4, 1) and (
) = (2, -5).
First find the midpoints of the given line segment.
M =
=
M =
Now, Find the slope of the line :
It is perpendicular to the line with (4,1) and (2,-5)
Slope between () and (
) =
so,
the slope between (4,1) and (2,-5) =
= 3
perpendicular lines have slopes the multiply to get -1
3 times m=-1
m=
The equation of a line that has a slope of m and passes through the midpoints M(3,-2) is
if we want slope intercept form
If we want standard form
Hence, Equation of a line is .
To learn more about perpendicular bisector of the line segment from the given link:
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Given:
The price of bananas can be determined by the equation P=0.25n, where P is the price and n is the number of bananas.
To find:
The constant of proportionality
Solution:
We have,
...(i)
where P is the price and n is the number of bananas.
Price P is directly proportional to the number of bananas. So,
...(ii)
Where, k is the constant of proportionality.
On comparing (i) and (ii), we get
Therefore, the constant of proportionality is 0.25.