# Thread: How to find possible formula for a function

1. ## How to find possible formula for a function

Please help me with a). I do not understand how to find the formula from the lines.

2. Originally Posted by florx

Please help me with a). I do not understand how to find the formula from the lines.
for g(x) you have been given two points (0,-1) and (3,0) where :

${x_1} = 0 , {y_1} = -1, {x_2} = 3, {y_2}=0$

you can find the function using this formula:

$(y - {y_1}) = \frac{{y_2}-{y_1}}{{x_2}-{x_1}} (x-{x_1})$

Do the same for f(x)

3. What would the "plain"(without the 1 or 2 next to it) x and y be in the formula (y - y1) = (y2-y1)/(x2-x1)*(x-x1)?

4. Originally Posted by florx
What would the "plain"(without the 1 or 2 next to it) x and y be in the formula (y - y1) = (y2-y1)/(x2-x1)*(x-x1)?
for g(x), your function will be:

$y-(-1) = \frac{0-(-1)}{3-0} (x-0)$

$y+1 = \frac{1}{3} x$

$y = \frac{x}{3} -1$

$\therefore g(x) = \frac{x}{3} -1 = \frac{x-3}{3}$

As instructed before, do the same for f(x).

Remember that you are using two-point form to find the equation(s) of the line(s).

Linear equation - Wikipedia, the free encyclopedia

5. Thank you so much for your continual help. I got the same answer using the
y = mx + b method.

Anyways should there be a limit on what x values these formulas should operate in? Because if there wasn't any, the lines will proceed to go further than the point of intersection between f(x) and g(x).

6. Originally Posted by florx
Thank you so much for your continual help. I got the same answer using the
y = mx + b method.

Anyways should there be a limit on what x values these formulas should operate in? Because if there wasn't any, the lines will proceed to go further than the point of intersection between f(x) and g(x).
Yes, the lines will go further beyond their point of intersection. The picture just shows a small portion of those two lines. Look at the graph given in the Wikipedia link.