Special Linear Relationships

Suppose y varies directly with x. If y = -4 when x = 8, what is the equation of direct variation? Complete the steps to write the equation of direct variation. Start with the equation of direct variation y = kx. Substitute in the given values for x and y to get___________________ Solve for k to get _________________Write the direct variation equation with the value found for k. The equation is________________________

1.✔ -4 = k(8)8 = k(-4). 2.✔ -1/2. 3.✔ y = (-1/2)x.

The pressure of a certain gas in atmospheres, p, and its corresponding volume in liters, v, are shown in the table. For the points in the table, does pressure vary directly with volume? If so, identify k and write an equation.

A. No, this is not a direct variation

Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) - 1.25 for n ≥ 1?

C).4, 2.75, 1.5, 0.25, -1, . . .

A recursive arithmetic sequence is defined as f(1) = 6, f(n+1) = f(n) + 5 for n ≥ 1. The first four terms of the sequence are shown in the table. Write an explicit formula that represents the sequence using function notation. Complete the steps to write an explicit formula that represents the sequence. Find the slope of the line that passes through the points given in the table. The slope is______________________ Use one of the given points to find the y-intercept. Substitute values for x, y, and m into the equation y = mx + b and solve for b. The y-intercept is__________________ Write the formula as a function of n in slope-intercept form. The function is _____________ for n in the set of natural numbers.

The slope is 5. The y-intercept is 1. The function is f(n) = 5n + 1

Which functions represent the arithmetic sequence 8, 1.5, -5, -11.5 . . . ? Check all that apply.

✔. f(n) = -6.5n + 14.5 ✔. f(1) = 8, f(n + 1) = f(n) - 6.5