Answer:
Step-by-step explanation:
Hello:
the equation is : y = ax+b
the slope is a : a×(2) = -1......( perpendicular to a line with a slope of 2 for : y=2x+1)
a =-1/2 y=(-1/2)x+b
the line that passes through (6, 2) : 2 = (-1/2)(6)+b
b = 5
the equation is : y = (-1/2)x+5
You can use the fact that perpendicular lines have slopes such that their multiplication ends up as -1.
The equation of the line perpendicular to line y = 2x + 1 and passing through (6,2) point coordinate is given as
[tex]y = -\dfrac{1}{2}x + 5[/tex]
Suppose that first straight line has slope 's'
Let another straight line be perpendicular to this first line.
Let its slope be 'a'
Then due to them being perpendicular, they have their slopes' multiplication as -1
or
[tex]s \times a = -1\\\\a = -\dfrac{1}{s}[/tex]
If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
[tex]y = mx + c[/tex]
The first line y = 2x + 1 is in slope intercept form and its slope is s = 2
Now, let the second line which is perpendicular to this line and passing through (6,2) coordinate be
y = [tex]ax + b[/tex]
Then as both lines are perpendicular, thus
[tex]a = -\dfrac{1}{s} = -\dfrac{1}{2}[/tex]
Thus, equation of second line is
[tex]y = -\dfrac{1}{2}x + c[/tex]
Since this line passes through coordinate (6,2), thus, this point coordinate should satisfy the equation of line as an equation is true for all points the graph represented by it passes through.
Thus,
[tex]y = -\dfrac{1}{2}x + c[/tex]
[tex]2 = -\dfrac{1}{2} \times 6 + c\\\\2 = -3 +c\\\\c=2+3 = 5[/tex]
Thus, equation of the second line is
[tex]y = -\dfrac{1}{2}x + 5[/tex]
Thus,
The equation of the line perpendicular to line y = 2x + 1 and passing through (6,2) point coordinate is given as
[tex]y = -\dfrac{1}{2}x + 5[/tex]
Learn more about slopes of straight lines here:
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