Rate of change , you are given the dollar value of a product in 2004 and the rate at which the value of the product is expected to change during the next 5 years. write a linear equation that gives the dollar value (v) of the product in terms of the year
(let t=0 represent 2000.)

2004 value= $156 with $4.50 increase per year

The linear equation is v = 4.5t +138

The product had value of $138 in 2000.

Step-by-step explanation:

In 2004, dollar value(v) = $156 and rate of change (m) = $4.50

The linear equation is in the form of y = mx + b, where "m" is slope or rate of change, b is the y-intercept.

We can rewrite the equation as v = m(t) + b.

Now let's find the value of b, when t = 4, m = 4.5, v = 156

156 = 4.5(4) + b

b = 156 - 4.5(4)

b = 156 - 18

b = 138

So, the linear equation is v = 4.5t +138

When t=0, the dollar value (v) = 4.5(0) + 138

v = $138

So, the product had value of $138 in 2000

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)