Equation of a Linear Relationship

[Dillinger4]

I just started Macro Economics and im having trouble calculation graphs. The Equation of Linear Relationship is stated as such.
dependent var = ver intercept + slope * independent var

Now going up the slope my calculations are always correct. 250 = 50 + .5(400), 125 = 50 + .5(150) but going down the result of the calculations are incorrect.

If we are on a downward slope then the slope is calculated as horizontal change / vertical change rather than vertical change / horizontal change. Correct? 400 = 50 + 2(250) is incorrect. So does the vertical intercept have to change also? But if that is the case then we would need a vertical intercept of -100?

[TheAlchemist]

hey mate,

your equation is the equation of a straight line....
y = mx + c where m = gradient, c = y intercept

it is derived from the definition of the gradient;
m = (change in y) / (change in x) = (y-y1)/(x-x1)

therefore m(x-x1) = y-y1
y = m*x - m*x1 + y1 = m*x + (y1- m*x1)

when x = 0, y = y1-m*x1, this is how we know it is the y intercept

if y1 and x1 are known then the whole thing can be reduced to the constant c. when m is negative, the function is a decresing one and when it is positive the function is an increasing one.

feel free to ask anything if you still don't understand.

[Dillinger4]

I figured it out. A direct relationship uses dependentvar = ver intercept + slope * independent var and an inverse relationship uses independentvar = verintercept + slope * dependentvar.

Since i am dealing with graphs there is no need to calculate the vertical intercept. Since the vertical intercept of a line is the place where it meets its vertical axis all i have to do is look at the graph.

[alkatran]

if I understand your question you want to find where two lines intersect.


as said above: Y = MX + B

The trick to finding it is making the equations = to each other. (both of them = to Y or 2Y etc...)


So, if, for example, they gave you:

2Y = 6X + 4
Y = .4X - 15

First, isolate Y (already done) and make it = to the Y in other equation:

2Y/2 = 6x/2 + 4/2
Y = 3x+2 and y= .4x - 15

No, now we know that: 3x+2 = .4x - 15

Isolate X:

3x-.4x + 2-2 = .4x/.4x-15-2
or
2.6x = -17

17/2.6 = ~6.53846...

So we know that the X where they intercept is 6.5, now we can find Y from either of the original equations

2Y = 6X + 4
2Y / 2 = ( 6(6.5) + 4) / 2
Y = 21.5

So they intercept at (6.5, 21.5)