Question

Find the direct variation equation which passes through (0, 0) and (4, 1).

y = 4x

y = -4x

y = 1/4 x

y = -1/4 x

Answer 1

You can start by finding its Slope...

Answer 2

\[Slope = \frac{y_2 - y_1}{x_2 - x_1}\]

Answer 3

1/4 is the slope

Answer 4

Right..

And equation is given by:

y = mx + c where m = Slope and c = y-intercept..

Answer 5

As this line is passing through origin or the line cuts y-axis at 0, hence c = 0..

Answer 6

So, your equation reduces to : y = mx

You know value of m here, so just put and find your equation.. :)

Answer 7

So, the answer would be y=1/4x? Since the c is 0?

Answer 8

Yep.. :)

Answer 9

Is the y intercept y1?

Answer 10

What??

Answer 11

Yes here you can say..

Answer 12

but how do you find the y intercept? (c)

Answer 13

Basically, y-intercept is the coordinate or length on y-axis where your line cuts y-axis.

Answer 14

Your given points are : (0,0) and (4,1) so try to graph them:

Answer 15

You can find it mathematically also, here is the method:

Suppose you are given with points : (3,4) and (4,2)

Find Slope first, Slope(m) = (2-4)/(4-3) = -2

Answer 16

Now, you know :

y = mx + c

And m = -2: so just put here:

so you get: y = -2x + c

Now, you should know this, if you know a point lying on your line, then that point should satisfy the equation of Line, I mean if line is passing through (2,4) then this point(2.4) should satisfy the equation of that line..

Answer 17

So, (3,4) point must satisfy your line equation..

y = -2x+c

Substitute that point here in this equation:
For point (3,4) : 4 = -2(3) + c \(c = 10\)

Answer 18

Similarly if you will put second point (4,2) in your equation, then also you must get the same value of c, try it..

Answer 19

Getting??

Answer 20

Dang, now I get it. This helped so much!!! Thank you tons

Answer 21

It is okay.. :)