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Answer:

y=0.5x-2

Step-by-step explanation:

if it is perpendicular to the line y=-2x-6, then you know that its slope is the negative reciprocal of that line, and it has a different y intercept which you need to solve for using the point given. You solve by plugging in the x and y values from the point and plugging in the slope into the standard equation, and solving for b, the y intercept

y=0.5x+b

1=0.5(6)+b

1=3+b

-2=b

The equation of the line that passes through the point (6, 1) and is perpendicular to the line whose equation is y=−2x−6  is y = 0.5x - 2.

How to find equation of straight line from concept of perpendicular line ?

From the classic definition of straight lines, we know that if we have to find an equation of a straight line being perpendicular to another straight line then the slope of the new equation of straight lines becomes negative reciprocal of the slope of given perpendicular line.

Finding the equation of the required straight line -

Mathematically, let m1 be the slope of the new straight line and m be the slope of the given perpendicular line, then we have

m1 = -(1/m)

Now, we have given equation y = -2x - 6

Thus slope of the required equation is say (m1) = -(-1/2) = 0.5

Thus the equation formed is y = (m1)x + c [where c is the y-intercept]

∴ y = 0.5x + c

The point given is (6,1) , thus y = 1 and x = 6

Thus the given equation can be formed as

⇒ 1 =  0.5*6 + c

∴  c = 1 - 0.5*6 = -2

The value of y-intercept of the required straight line is -2

The equation of straight line formed is y = 0.5x - 2.

Thus the equation of the line that passes through the point (6, 1) and is perpendicular to the line whose equation is y = − 2x − 6  is y = 0.5x - 2.

To learn more about equation of straight line, refer -

https://brainly.com/question/7669240

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