HOW TO WRITE LINEAR FUNCTION FROM GRAPH

use the graph to write an equation of the line and interpret the slope

Problem 1 :

Solution :

From the given figure above, by marking two points we get (0, 0) and (10, 2).

Slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - 0) / (10 - 0)

= 2/10

= 1/5

Interpreting the slope :

For every $5 increase of cost of meal, there will be $1 increase in tip.

Problem 2 :

Solution :

From the given figure rise = 3, run = 90

Falling line will have negative slope.

Slope = Rise / Run

= -3/90

= -1/30

Interpreting the slope :

So, car using 1 gallon of gasoline for every 30 miles. 

Problem 3 :

Solution :

From the given figure rise = 6, run = 4

Raising line will have positive slope.

Slope = Rise / Run

= 6/4

= 3/2

Interpreting the slope :

For every 2 years increase, the tree will grow 3 feet.

Problem 4 :

Solution :

From the given figure rise = 100, run = 2

Raising line will have positive slope.

Slope = Rise / Run

= 100/2

= 50/1

Interpreting the slope :

For every 1 week increase, balance will increase $50.

Problem 5 :

Solution :

Selecting two points from the straight line, let (1, 55) and (3, 165).

Raising line will have positive slope.

Slope = (y₂ - y₁) / (x₂ - x₁)

= (165 - 55) / (3 - 1)

= 110/2

= 55/1

Interpreting the slope :

For every 1 minute, she will type 55 words.

Problem 6 :

Solution :

Selecting two points from the straight line, let (3, 300) and (5, 180).

Falling line will have negative slope.

Slope = (y₂ - y₁) / (x₂ - x₁)

= (180 - 300) / (5 - 3)

= -120 / 2 

= -60/1

Interpreting the slope :

For every 1 hour, the volume will decrease at the rate of 60 cubic feet.

Problem 6 :

Two newspapers charge a fee for placing an advertisement in their paper plus a fee based on the number of lines in the advertisement. The table shows the total costs for different length advertisements at the Daily Times.

The total cost y (in dollars) for an advertisement that is x lines long at the Greenville Journal is represented by the equation

y = 2x + 20.

a) Which newspaper charges less per line?

b)  How many lines must be in an advertisement for the total costs to be the same?

Solution :

Choosing two points from the table, say (4, 27) and (5, 30)

Slope = (y₂ - y₁) / (x₂ - x₁)

= (30 - 27) / ( 5 - 1)

= 3/1

Rate of change in daily times = 3

Applying the slope in y = mx + b, we get

y = 3x + b

Choosing one of the points from the table say (6, 33)

33 = 3(6) + b

33 = 18 + b

b = 33 - 18

b = 15

y = 3x + 15

Comparing the given equation y = 2x + 20 with y = mx + b

m = 2

Rate of change for Greenville = 2

a) Cost of Green ville is charging less per line.

b) When the total cost will be same,

y = 3x + 15 ----(1)

y = 2x + 20 ----(2)

(1) = (2)

3x + 15 = 2x + 20

3x - 2x = 20 - 15

x = 5

When the number of lines is 5, then the cost will be equal.