3 wks ago company had 250 clocks in inventory, 2 wks from now it will have 500 - what is the expression for it

Question

3 weeks ago a company had 250 clocks in inventory.  2 weeks from now it will have 500.  I need an algabraic equation for this using the Y=mx+b to determine the y intercept and the y2-y1, x2-x1 formulations.

Answer 1

Let x = time (weeks)

Let y = number of clocks

 

Three weeks ago can be written as x = -3

Two weeks from now can be written as x = 2

 

We now have two points: (-3, 250) and (2, 500)

 

Slope = m = (y₂-y₁)/(x₂-x₁) = (500-250)/(2 - (-3)) = 250/5 = 50.

 

Equation of a line in slope-intercept form: y = mx + b

 

Solve for b using point (2, 500)

 

500 = 50(2) + b

500 = 100 + b

b = 400

 

So, equation of line (slope-intercept form) is y = 50x + 400.

 

y-intercept = b, so point is (0,400)

 

Equation of line in point-slope form is y-y₁=m(x-x₁)

Since slope m = 50,

     y-y₁=50(x-x₁)

 

Pick one point for (x₁,y₁).  Use (2,500).

 

Equation of line (point-slope):  y-500= 50(x-2)

 

Hope this helps!

 

 

 

Answer 2

I agree in general... but shouldn't your first ordered pair be (-3, 250)?

 

slope would be (500 - 250)  =250 = 25

                         2 - (-3)         5

  

y = 25x + b

500 = 25 (2) + b

450 = b

therefore: y=25X + 450

Answer 3

Let x = weeks from now and y = the number of clocks.  We have two known points on the line:

1. (-3,300)       3 weeks ago company had 250 clocks in inventory
2. (2,500)        2 weeks from now it will have 500 clocks in inventory

 

The slope, m, is:

 

m = (y₂-y₁)/(x₂-x₁)

m = (500-300)/(2-(-3)) = 200/5 = 40

 

Hence the equation so far is:

 

y = 40x + b

 

To find b, plug in the x and y values from either known point and solve for b.  I'll use (2,500):

 

y = 40x + b

500 = 40*2 + b

500 = 80 + b

420 = b

 

So our final equation is:

 

y = 40x + 420