GRAPH A LINE USING X AND Y INTERCEPTS

Use axes intercepts to draw the graph of:

Problem 1 :

x + y = 6

Solution :

Plot (6, 0) and (0, 6) by connecting these two points, we will get the line.

Problem 2 :

2x + y = 4

Solution :

Plot (2, 0) and (0, 4) by connecting these two points, we will get the line.

Problem 3 :

3x - y = 5

Solution :

Plot (5/3, 0) and (0, -5) by connecting these two points, we will get the line.

Problem 4 :

2x + 3y = 6

Solution :

Plot (3, 0) and (0, 2) by connecting these two points, we will get the line.

Problem 5 :

3x - 4y = 12

Solution :

Plot (4, 0) and (0, -3) by connecting these two points, we will get the line.

Problem 6 :

x + 3y = -6

Solution :

Plot (-6, 0) and (0, -2) by connecting these two points, we will get the line.

Problem 7 :

2x - 5y = 10

Solution :

Plot (5, 0) and (0, -2) by connecting these two points, we will get the line.

Problem 8 :

2x + 7y = 14

Solution :

Plot (7, 0) and (0, 2), by connecting these two points, we will get the line.

Problem 9 :

3x - 4y = 8

Solution :

Plot (8/3, 0) and (0, -2),  by connecting these two points, we will get the line.

Problem 10 :

You are designing a sticker to advertise your band. A company charges $225 for the first 1000 stickers and $80 for each additional 1000 stickers.

a. Write an equation that represents the total cost (in dollars) of the stickers as a function of the number (in thousands) of stickers ordered.

b. Find the total cost of 9000 stickers.

Solution :

a) Let x be the number of stickers and y be the charge.

(1000, 225) and (2000, 305)

Slope = (y₂ - y₁) / (x₂ - x₁)

= (305 - 225) / (2000 - 1000)

= 80/1000

= 2/25

Equation of line :

(y - y₁) = m(x - x₁)

(y - 225) = (2/25)(x - 1000)

y = 2x/25 - (2/25) ⋅ 1000 + 225

y = 2x/25 - 2 ⋅ 40 + 225

y = 2x/25 - 80 + 225

y = 2x/25 - 145

b) Total cost of 9000 stickers.

y = 2(9000)/25 - 145

= 720 - 145

= 575

So, the required cost is $575.

Problem 11 :

You pay a processing fee and a daily fee to rent a beach house. The table shows the total cost of renting the beach house for different numbers of days.

a. Can the situation be modeled by a linear equation? Explain.

b. What is the processing fee? the daily fee?

c. You can spend no more than $1200 on the beach house rental. What is the maximum number of days you can rent the beach house?

Solution :

Let be the number of days and y be the total cost

(2, 246) and (4, 450)

Slope = (y₂ - y₁) / (x₂ - x₁)

= (450 - 246) / (4 - 2)

= 194/2

= 97

Equation of line :

(y - y₁) = m(x - x₁)

(y - 246) = 97(x - 2)

y = 97x - 194 + 246

y = 97x + 52

b) Processing fee is $52 and daily fee is $97.

c) Amount spend = 2000

2000 = 97x + 52

97x = 2000 - 52

97x = 1948

x = 1948/97

x = 20.08

Approximately 20 days.