find the equation of the line through (4,3) and (2,4). Then write the equation in standard form.?

Answer 1

equation of line through (4,3) and (2,4) is 2y=-x+10

Answer 2

The standard form is: y - y1 = m(x - x1)

so you have the coordinates: (4,3) and (2,4)
let the coordinates (4,3) be (x1, y1) and let (2,4) be (x2, y2)

first, find the gradient (m)
m = (y2 - y1)/(x2 - x1)
m = (4 - 3)/(2-4)
m = 1/(-2)
m = -1/2 (minus half)

now, substitute the known values into the general form equation:
y - y1 = m(x - x1)
y - 3 = -1/2(x - 4)
y - 3 = -x/2 + 4
y - 3 + x/2 -4 = 0 (bring everything to one side)
y + x/2 - 7 = 0

so your answer is: y + x/2 - 7 = 0

Answer 3

For the first X+3=7 and 4+Y=7
and for the second X+4=6 and 2+Y=6

Answer 4

First solve for slope.

slope formula

s = y₂- y/ x₂- x₁

Ordered Pair

P(2.4) Q(4, 2)

s = 4 - 3/ 2 - 4

s = 1/-2

s= - 1/2

The answer is s = - 1/2

Insert the s value into the slope Intercept form of the equation of a line.

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Slope Intercept form of the equation of a line

Oredered Pair

P(2.4)

y = mx + b

4 = - 1/2(2) + b

4 = -1 + b

4 + 1 = - 1 + b + 1

5 = b

The answer is b = 5

Insert the b value into the equation

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The equation in standard form becomes

y = - 1/2(2) + 5

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Answer 5

1st find slope of line.

Slope (m) = (y2 - y1) / (x2 - x1)
Slope (m) = (4 - 3) / (2 - 4) = - ½

Equation of line :
y - y1 = m(x - x1)
y - 3 = -½(x - 4)
y - 3 = -½x +2
y = -½x + 2 + 3
y = -½x + 5 Standard form.

This equation may be doubled up to get rid of the fraction.
2y = -x + 10

Answer 6

A(x1,y1) --->A(4,3)
B(x2,y2) --->B(2,4)
The equation of the line through points A , B is:
y-y1=m(x-x1) or y-y2=m(x-x2)
where m=(y2-y1)/(x2-x1) (is line slope)
therefore :
y-3=((4-3)/(2-4))(x-4) ---> y-3=(-1/2)(x-4) ---> y-3= -x/2+2 --->
y= -x/2+5.
line equation: y= -x/2+5

Answer 7

m= [y2 - y1] / [x2 - x1]

m = [4-3] / [2-4] = -1/2

using [4,3] and m= -1/2

4=-1/2*2+b
4=-1+b
b = 5

So y = -1/2x+5

Answer 8

Find gradient of two points.
g= Change in Y divide by Change in X

Change in Y = 3 - 4 = -1
Change in X = 4 - 2 = 2
g=-0.5

y=mx + c
y=-0.5x + c (Find value of C)

Input any point to find value of C:
3 = (-0.5)(4) + C
C= 5

Therefore: y=-0.5x + 5

Answer 9

well, everyone else did the work, so i'll just put the answer in standard form...

x + 2y = 10

take what someone else did and then write it as i did above so you can have the answer in standard form.

Answer 10

x-4/4-2=y-3/3-4
x-4/2=y-3/-1
-x+4=2y-6
x+2y-10=0