Can anyone find any equation of the line containing the point (-2, 6) and perpendicular to the line 2x +y = 5?

Question

Can anyone find any equation of the line containing the point
(-2, 6) and perpendicular to the line 2x +y = 5?

Answer 1

y=1/2x + 7

flip and take the reciprocal of the slope and plug in the points to find the new y-intercept

Answer 2

The equation 2x + y = 5 can be rearranged into y = -2x + 5. This means that the line has slope of -2. For a slope perpendicular to this, we use the negative recipricol. This is essentialy -1/m where m is the original slope. So in this case the perpendicular slope will be -1/-2 which is 1/2.

Now the equation of the new line is:

y = 1/2x + b

You are given point (-2 , 6) which you can substitute in to find b which becomes 7.

So the equation is y = 1/2x + 7

Hope this helps!

Answer 3

The given line is expressed as y = -2x + 5, so the slope is -2.

A line perpendicular to this would have a slope of 1/2.

1/2 = (y - 6) / (x + 2)
1/2(x + 2) = y - 6
1/2x + 1 = y -6
x/2 - y = -7

Answer 4

Your equation is at present in often happening style: mx + ky = b (with ok being a relentless, m slope, and b y-intercept). In slope-intercept style, it could be y=-2x+5. (y=mx+b) To get a perpendicular line, take the damaging reciprocal. that's, multiply the slope (to that end -2) by using -a million, and turn it the different way up. So -2/a million will exchange right into a million/2. that's our new slope. perfect now, our equation is y=(a million/2)x+b. to locate b, basically plug the given coordinates into the hot equation and clean up for b. (keep in mind that b is the place the hot line intersects the y-axis. this could be a stable verify to make particular you solved for b wisely, by using graphing your new equation.) 6=(a million/2)(-2)+b 6=-a million+b b=7 Plug b returned into the equation to get your answer: y=(a million/2)x+7. Simplified it could be y=x/2 + 7.

Answer 5

the product of the slopes of two perpendicular lines are -1.

to find the slope, take y alone and then the slope is the number in front of x:
y=-2x+5 (slope is -2)

means, the slope of the line you're looking for is 1/2.

means, the equation is y= (1/2 x) + c

since you have a point, the point will give you the value of c

x=-2 and y=6

6=-1+c

c=7

then the line is

y= (1/2 x) +7

Answer 6

Put the equation in slope-intercept form:
y=mx+b
Subtract 2x from both sides:
y=-2x+5
The slope is -2, but you want the reciprocal of that slope, so that slope is 1/2.
The next step is to use the point-slope form:
y-y1=m(x-x1)
y-6=1/2(x+2)
y-6=1/2x+1
y=1/2x+7

Answer 7

(y-y1)=m(x-x1)

Put original equation in form y=mx+b

y=-2x+5
m=-2
perpendicular is the negative reciprocal of the slope
m=1/2

Plug point and new slope into point slope formula.
y-6=(1/2)(x+2)
simplify
y-6=(1/2)x+1

y=(1/2)x+7

Answer 8

y=1/2x+7