Is it true that a linear equation determines a line in the x-y plane

True

Step-by-step explanation:

A linear equatin in the xy plane contains two variables x and y and the power of both x and y should always be 1

The std form of a linear equation is

ax+by+c =0

Let us prove that this repesents a straight line only.

Consider the equation ax+by+c=0

Differentiate wrt x

a + b y' =0

Or y' = -b/a

In other words the slope of the curve is not dependent on the points taken but constant.

This ensures constant variation of y over x.

Hence this is nothing but a straight line in xy plane.

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.