Find equation in standard form, with all integer coefficients, of the line perpendicular to x – 2y = 24 a?

Question

Find the equation, in standard form, with all integer coefficients, of the line perpendicular to x – 2y = 24 & passing through (1, 3)

Answer 1

First, you solve for the line in y-intercept form:

x - 2y = 24
-2y = -x + 24
y = (1/2) x - 12

So our slope of the line is 1/2. Remember that in order to find the line perpendicular, you have to take the "negative reciprocal" of the slope. In our case, since m = 1/2, the negative reciprocal of the perpendicular line will be m = -2

Thus, our equation is y = -2x + b

Then we use the "slope = slope" method of calculating the line with the given points (1,3), to get

(y - 3)/(x - 1) = -2
y-3 = -2(x-1)
y-3 = -2x + 2
2x + y - 5 = 0 (which is now in standard form)

Answer 2

Heres how i would do it:
solve equation for y:
x - 2y = 24
+2y +2y
x = 2y+24
-24 -24
x-24 = 2y
divide both sides by 2... (same thing as multiplying both sides by (1/2) )
(1/2)x - 12 = y

perpendicular means that if the line has the slope is (a/b), the slope of the line perpendicular to the first line is -(b/a).
Therefore:
original slope = (1/2) so
perpendicular slope = -(2/1) or just -2

so far, your equation is y = -2x+b (b = y-intercept)
to find y-intercept:
plug in the point (1,3) for x and y in the equation
3 = -2(1) + b
3 = -2 +b
+2 +2
5 = b

so in slope intercept the equation is y = -2x+5
NOW to put it in standard form:
y = -2x+5
+2x +2x
2x + y = 5

and you are finished!!!!!!!!!

Answer 3

A perpendicular line has a negative reciprocal slope. This means in perpendicular lines, m * n = -1 where m is the slope of one line and n is the slope of the other. The slope is easily discernible in y = mx + b form (in which m is the slope). So first manipulate this equation a bit.

x - 2y = 24
::subtract an x from both sides
-2y = -x + 24
::divide by -2
y = 1/2x - 12

From this, we can see that the slope of this line is 1/2. The negative reciprocal of 1/2 is -2. Then, we write an equation using this slope and the point given. We utilise point-slope form in this instance.

y - y of point = m (x - x of point)
y-3 = -2 ( x-1)
::change into standard form
y-3 = -2x +2
y+2x=2+3
2x + y = 5 is your answer.

Answer 4

First, find the gradient of that line: 2y = x-24, so y = 0.5x - 12, so the gradient is 0.5.

Thus the gradient of a perpendicular line is -1/0.5 = -2.

So the line is of the form y = -2x + c
Substitute in the point to get 3 = -2 + c, so c = 5, and the equation is y = -2x + 5.
Or 2x + y = 5.

Answer 5

To get the necessary negative reciprocal slope, reverse the x and y coefficients and the sign between, getting 2x + y = ....

and then plug in the point. 2(1)+3 = 5.

So 2x + y = 5.

Answer 6

x-2y=24
-2y=-x+24
y=x/2-12
slope is 1/2
slope of perpindicular is -2
y=-2x+b
3=-2+b
b=5
y=-2x+5
2x+y=5