Question

(0.5 point) (1)The slope of a vertical line is Table Books Book Price Sales $ 100 $ 100 Book price (P) 20 f 16 Sales (0)12 (2) Use the following data to find the slope of this line. (0.5 point) Correct Work (1.5 points) (3) In complete sentences, explain and interpret what does the numeric value of this slope mean in respect to price and sales of book? (Hint: refer to our class lecture/notes.) (2 points) 4. Assume the data above corresponds to the following equation: y = a + bx. Fill in the values for a and b. Price (Y) Quantity (x) 29 -1 24 | 191 14 9 4 (correct work 0.75 pt & correct answer 0.25pt)

Answer 1

(a) The slope of vertical line is undefined.

(b) Slope = (vertical change / horizontal change)

Movement from point a to point b leads to change in book price from 100 to 80 (note: book price measured on the Y-axis) and sales changes from 0 to 4 (note: sales measured on the X-axis)

Slope = (80 - 100) / (4 - 0)

Slope = -20 / 4

Slope = -5

Slope of this line is -5.

(c) Slope of this line is -5. It reflect that every 1 unit increase in sales leads to decrease in books price by 5.

(d) y = a + bx

Where, y is the dependent variable (price)

x is independent variable (quantity)

a is intercept value (the value of y when x is 0)

b is slope .

From the given table we can find that the value of "a" is 24.

Slope = (change in price / change in quantity)

Change in price from 24 to 19 leads to change the quantity from  0 to 1.

Slope = (19 - 24) / (1 - 0)

Slope = -5/ 1

Slope = -5.

Hence, the value of "b" is -5.

y = 24 + (-5)x

y = 24 - 5x