Aline passes through (2,-1) and (4,5)
which answer is the equation of the line.
a: -3x+5y=-13
b: -3x+y=-7
c: -3x+5y=13
d: -3x+y=17

Step-by-step explanation:

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

The line passes through (2,-1) and (4,5),

y2 = 5

y1 = - 1

x2 = 4

x1 = 2

Slope,m = (5 - - 1)/(4 - 2) = 6/2 = 3

To determine the intercept, we would substitute x = 4, y = 5 and m= 3 into y = mx + c. It becomes

5 = 3 × 4 + c

c = 5 - 12 = - 7

The equation becomes

y = 3x - 7

(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.