Write the equation of the line that passes through the given point and is perpendicular to the given line. Your answer should be written in slope-intercept form. P (3,-4),x= - 7/8y+3

y = 7x/8 - 53/8

Step-by-step explanation:

P(3,-4)

x = -7y/8 + 3

Isolate y and translate to slope-intercept form:

y = mx + b

x = -7y/8 + 3

x - 3 = -7y/8

8x - 24 = -7y

y = -8x/7 - 24/7

The slope of the equation is -8/7

The slope of the new equation will be perpendicular to the slope of the given equation which means it is the negative reciprocal.

y = mx + b where m = -1/(-8/7) = 7/8

y = 7x/8 + b

Plug in know values and solve for b:

-4 = 7(3)/8 + b = 21/8 + b

-4 - 21/8 = b

b = -32/8 -21/8 = -53/8

Plug in b into the equation:

y = 7x/8 - 53/8

(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.

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