how do u make an equation from a given line?

Question

if you are given a line on a graph..how are you supposed to find the equation of the line.

i have a line on a graph that passes through 12 on the y axis and 36 on the x axis..there is a point on the line at (18,6)...how do i find the equation of the given line?

Answer 1

If I'm reading the question correctly, you have three points, which is one more than you need. Your points are

(0, 12)
(36, 0) and
(18, 6)

The easiest way to get the equation is to put it into slope-intercept form, because you already have the y-intercept. As you should know, slope intercept is

y = mx + b

where m is the slope and b is the y-coordinate of the y-intercept. You know that b is 12, so all you need is m.

The slope formula is

m = (y2 - y1)/(x2 - x1)

Pick two of your points - which you pick doesn't matter - and plug in. Lets use your intercepts. Then you have

m = (12 - 0)/(0 - 36) = 12/(-36) = -(1/3)

So your equation is

y = -(1/3)x + 12

Checking that against your other given point, we have

y = -(1/3)(18) + 12 = -6 + 12 = 6

which fits.

Answer 2

let (x1,y1) and (x2,y2) be two points on the line....

then the formula for equation of the line is

(x - x1) / (x2 - x1) = (y - y1) / (y2 - y1)

(x is X, x1,x2,y1,y2 are points.

For ur question the answer is
(x - 18)/(36 - 18) = (y - 6)/(12 - 6 )
=> (x - 18) / 18 = (y - 6)/6
=> (x -18) = 18*(y - 6)/6 (now 18/6 = 3)
there fore => x - 18 = 3(y - 6)
is the required equation.

Answer 3

Use Pythagorus theorem to find the eqation of the line.

Answer 4

find a theme.

Answer 5

hey, it's always better to do the homework yourself...