Question

ok if my points are (y108,000, x2.0) and (y96000, x4.0) I need to find the slope of the line and put it into an equation.

Answer 1

Slope : \[\frac{f(x) - f(x')}{x-x'}\]

Just fill the correct value given in this generic formula.

Answer 2

Once the slope in found, your (assumed linear) function will be :

\[f(x) = \text{slope} \times x + \text{offset at (0,y)}\]

Answer 3

To find the offset, just use solve this simple equation with the data you have : \[y = a \times x + b \rightarrow b = y + a \times x\] (with a : slope, and b : offset)

Answer 4

lol.. thank you, but I'm still lost on how to get the slope. I suck at math royally. .. my work says to find the slope of the line and then find the linear equation in slope intercept form

Answer 5

Ok, I'll give a numerical example with your data.

Answer 6

Your data are :
\[f(2) = 108000 \text { and } f(4) = 96000\]

Plug the two in the slope equation :
\[\frac{f(4) - f(2)}{4 - 2} \equiv \frac{96000 - 108000}{2} \equiv \frac{ -12000}{2} \equiv -6000 \]

Your slope is -6000.

The general equation of a linear function is :

\[y = f(x) = a x + b \text{ and with your slope : } y = f(x) = -6000 x + b\]

Solv ethe equation to find b, the offset at origin (don't know what you call it, that's how oit is named here in France) :

\[y = -6000 x +b \equiv b = y + -6000x \text{ , so we fill with the data : }\]
\[b = 96000 + -6000 \times 4 = 72000\]

So the formula is :

y = -6000x + 72000