Question

What is the equation of a line that passes through the point (6, 1) and is perpendicular to the line whose equation is y=−2x−6 ?

Answer 1

y = 1/2x - 2

Look at Desmos Math pic i sent.

Answer 2

Answer:

y = $\frac{1}{2} x$  +   3

Step-by-step explanation:

To find the equation that passes through the points (6,1) and is perpendicular to the line whose equation is y = -2x - 6, we are going to follow the steps below;

First, we determine the slope of the equation:y = -2x - 6, only then can we find the slope of our perpendicular equation.

y = -2x - 6

m = -2

The slope of the above line is   -2

So, the slope of the perpendicular line to y = -2x - 6 will have a slope equals to the negative reciprocal , that is;  $m_{1} m_{2}$   =   -1

      The slope(m) of our perpendicular equation is $\frac{1}{2}$ using the above formula.

Haven gotten our  slope, next is for us to find our intercept

To get the intercept, we will use this standard equation;

y = mx + c

where m =slope(our new slope=1/2)   c=intercept   x and y are the two points through which the line passes through. That is; x=6 and y=1. So we are going to plug in all this variable into the standard equation;

y = mx + c

1  =  $\frac{1}{2}$(6)  +   c

1  =  3  +  c          (six will divide two to give us three)

To get the value of c, subtract 3 from both-side of the equation

1 - 3  =  3+ c -3

-2  =   c

c = -2

Therefore, our new intercept is 3

So we can now plug in our new slope and intercept into y=mx+c

y = $\frac{1}{2} x$  +   3

We can re-arrange it;

- $\frac{1}{2} x$ + y  =  3