Linear Models and Systems of Eqns (2.1 - 2.4)

When x_{1 =} x₂ the slope is…

Undefined

When y_{1 =} y₂ the slope is…

Zero

The equation of a horizontal line is…

y = b

The equation of a vertical line is…

x = a

What form is y - y₁ = m (x - x₁)

Point Slope Form

What form is y = mx + b

Slope Intercept Form

What form is Ax + By = C

Standard Form (General Form)

Standard form must always have A, B, and C as…

Integers

Intercepts should always be presented in what format?

Point: (x, y)

Values that can be put into a function are the _____ of a function.

Domain

Values that are output from the function are the _____ of a function.

Range

Linear Depreciation

V(t) = mt + b

The b in V(t) = mt + b represents the…

Purchase Price

The “rate of depreciation” is…

The absolute value of the slope, |m|

Scrap value (V_s) is…

The lowest value an asset obtains.

Scrap time (V_t) is…

The x-value when the asset is fully depreciated.

If V(t) is ever less than V_s then…

It is equal to the scrap value, V(t) = V_s

The total cost function, C(x), models… and includes both…

The total cost of producing items, variable and fixed costs

The function for total cost is…

C(x) = mx + F or Total Cost = (production cost per item)(quantity) + (Fixed Cost)

Revenue, R(x), models…

The amount of money a company brings from sales.

The function for revenue is…

R(x) = p(x) or Revenue = (price per item)(quantity)

Profit, P(x), models… and includes both…

The amount of money a company brings in after expenses, Revenue R(x) and Total Cost C(x)

The function for profit is…

P(x) = R(x) - C(x) or Profit = Revenue - Total Cost

Both the supply and demand curves are _____ curves.

Price, p(x)

The supply and demand curve is… where y = _____ and x = _____.

p(x) = mx + b, price and quantity demanded

The slope for a demand curve is always…

m < 0

The slope for supply curve is always…

m > 0

An independent system has ________ solution(s)

Exactly one

An inconsistent system has ________ solution(s)

No

A dependent system has ________ solution(s)

Infinite

The conditions for an independent system are…

m₁ = m₂ (one point of intersection)

The conditions for an inconsistent system are…

m₁ = m₂ but b₁ not equal to b₂ (parallel lines)

The conditions for an dependent system are…

m₁ = m₂ and b₁ = b₂ (same line)

The break-even point is where…

Revenue equals the costs, R(x) = C(x)