Cartesian Coordinate System and Straight Line

1. Determine which, if any, of the ordered pairs listed satisfy the given equation.

1.1. 2y-4x = 10; a. (7,1) b. (1,7) c. (5,0)

1.2. 3x + 2y = 12; a. (2,3) b. (0,6) c. (3,0)

2. Find a general linear equation ( Ax + By = C) of the straight line that has the indicated properties and sketch each line by defining x-intercept , y-intercept , or both.

a. Passes through origin and has slope -5.

b. Has slope 0 and y-intercept .

c. Is horizontal and passes through (-3, -2).

d. Is vertical and passes through (-1,4).

e. Passes through (3,-1) and (-2, -9).

3. Find, if possible, the slope, x-intercept, and y-intercept of the straight line determined by the equation, and sketch the graph.

3x-2y = 10

4. Find an equation of the line passes through (-3,2) and is parallel to 2x +3y = -6

5. Determine whether the lines are parallel, perpendicular, or neither. Also specify your reason.

(a) y = 3, x =-1/3

(b) 3x + y = 4, x-3y+1=0

6. A house purchased for $198,000 is expected to double in value in 18 years. Find a linear equation that describes the house’s value after x years.

7. Suppose consumers will demand 40 units of a product when the price is $12 per unit and 25 units when the price is $18 each. Find the demand equation, assuming that it is linear. Find the price per unit when 30 units are demanded.

8. Suppose a pizza company has a fixed cost of $500 and a total cost of $550 for total production of 100 slices of pizza.

(a) Assume that the total cost equation is linear in quantity. Write a total cost equation in relation to total pizza production. Let y be the total cost and x be the total production.

(b) What is the slope of total cost equation? How would you interpret the slope of the total cost equation?