Scatter plots and prediction equations?....explain?

Question

cost of 200 sq ft of storage space is $60. the cost of 325 sq ft is $160.

1. find prediction equation

2. find slope of prediction equation

3.preict number of sq ft for storage costing $44.

Answer 1

Let y = f(x) = cost in dollars where x is the square feet of storage space.

The equation of a straight line is y = mx + b where b is the slope and b is the y-intercept (i.e., where x = 0).

The slope of a line is found by (y2 - y1) / (x2 - x1).

(x1,y1) = (200,60) and (x2,y2) = (325, 160)

Slope = (160 - 60) / (325 - 200) = 100 / 125 = 0.800

So far our line equation is y = 0.800x + b.

To find b, plug in one of the two points (I'll use (x1,y1)).

y = 0.800x + b

60 = 0.800 (200) + b

60 = 160 + b

-100 = b

So our prediction equation is y = 0.800x - 100.

Itf the cost (y) is $44, then x (square feet) is:

y = 0.800x - 100

44 = 0.800x - 100

144 = 0.800x

144 / 0.800 = x = 180 ft^2.

Answer 2

The equation for a line is

y = ax + b  (among others) where 'a' is the slope.

We know that:

60 = a(200) + b

160 = a(325) + b

Subtracting the first equation from second to remove b:

100 = a(125)

a = 100/125 = 0.8 <=== The slope In $ per sq ft.

Then, use a to find b in the first equation:

60 = .8(200) + b

b = 60 - 160

b = -100 <=== The y intercept in dollars

So the equation is y = .8x -100

For the last:

44 = 0.8x -100

x = (44+100)/.8 = 180 square feet.

Answer 3

Assume it's a linear relationship meaning it's a straight line.

Let y be cost in $, x be area in sq ft.

(y-60)/(x-200) = (160-60)/(325-200) = 4/5

y-60 = (4/5)(x-200)

y = (4/5)x - 100

slope=4/5

44 = (4/5)x - 100

144 = (4/5)x

x = 180