Find the standard form of the equation of the line that passes through the points (4, -8) and (2, -3).?

Question

I really just need to know how to find the equation.....I know how to change it to standard form.

Answer 1

Well, you know the m in y=mx+b is the slope of a linear line. In order to find slope, m, we can use the formula m= y2-y1/x2-x1, where x1,x2,y1,y2 are x points and y points in a line, so we have m= -3+8/2-4 = -5/2

To solve for b, we choose a point on the line, say, (4,-8), and plug it into the y=mx+b equation, so we get
-8=(-5/2)4+b
-8=-10+b
b=2

So our equation for the line is
[Answer: (5/2)x + y = 2] or
[Answer: 5x + 2y = 4] (multiply everything in the answer above by 2)

Answer 2

well... lets take a crack at it..

firstly we find the slope of the equation, passing through both points.

so that we get m = (-3+8)/(2-4) = - 5/2

secondly we use the point slope formula
namely y-y1= m(x-x1).. where here, (x1, and y1) are a point chosen from the two given.. lets choose (4,-8)..

to get y+8 = -5/2 (x-4).. from which you can put into the Standard form

Ax +By = C..

which you can do!!... hope that helps..

Answer 3

Let's choose a point and calculate slope in one equation as follows:

(y+3) / (x-2) = (-3-(-8)) / (2-4)

(y+3) / (x-2) = 5/(-2)

Cross multiplying and simplifying gives

y = -5/2(x) + 2

Answer 4

Vector thas passes through the points:
(4, -8) - (2, -3)
V = (2, -5)

Continuous form:
(x - xo) / vx = (y - yo) / vy
(x - 2) / 2 = (y - (-3)) / (-5)
-5 * (x - 2) = 2 ( y + 3)
-5x + 10 = 2y + 6
-5x - 2y + 4 = 0
5x + 2y - 4 = 0

Bye and happy new year