GRAPHING FROM A TABLE TO WRITE AN EQUATION

We can use information from a table to draw a graph of a linear relationship and to write an equation for the graphed line.

Example 1 : 

The table shows the temperature of a fish tank during an experiment. Graph the data, and find the slope and y-intercept from the graph. Then write the equation for the graph in slope-intercept form.

Solution : 

Step 1 : 

Ordered pairs from the table (time, temperature) :

(0, 82), (1, 80), (2, 78), (3, 76), (4, 74) and (5, 72). 

Plot the above points (ordered pairs) on a graph paper. 

Step 2 : 

Connect all the points which have been plotted on a graph paper. 

Step 3 : 

Choose any two points on the line to find the slope :

For example, let us choose (0, 82) and (1, 80).

Use the slope formula. 

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute : 

(x₁, y₁)  =  (0, 82)

(x₂, y₂)  =  (1, 80)

Then, 

m  =  (80 - 82) / (1 - 0)

m  =  2 / 1

m  =  2

Step 4 : 

Read the y-intercept (b) from the table or graph.

That is, the value of 'y' when x = 0.

or 

The level of temperature when time = 0.

b  =  82

Step 5 : 

Now, we can use the slope and y-intercept values to write  equation of the line in slope-intercept form.

The slope-intercept form equation of a line is

y  =  mx + b

Substitute  m  =  2 and b  =  82.

y  =  -2x + 82

Example 2 : 

The table shows the temperature of a fish tank during an experiment. Graph the data, and find the slope and y-intercept from the graph. Then write the equation for the graph in slope-intercept form.

Solution : 

Step 1 : 

Ordered pairs from the table (time, temperature) :

(0, 75,000), (10, 150,000), (15, 225,000), (20, 300,000) 

Plot the above points (ordered pairs) on a graph paper. 

Step 2 : 

Connect all the points which have been plotted on a graph paper. 

Step 3 : 

Choose any two points on the line to find the slope :

For example, let us choose (5, 75,000) and (10, 150,000).

Use the slope formula. 

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute : 

(x₁, y₁)  =  (5, 75000)

(x₂, y₂)  =  (10, 150000)

Then, 

m  =  (150,000 - 75,000) / (10 - 5)

m  =  75,000 / 5

m  =  15,000

Step 4 : 

Read the y-intercept (b) from the table or graph.

That is, the value of 'y' when x = 0.

or 

The volume of water when time = 0.

b  =  0

Step 5 : 

Now, we can use the slope and y-intercept values to write equation of the line in slope-intercept form.

The slope-intercept form equation of a line is

y  =  mx + b

Substitute  m  =  15,000 and b  =  0.

y  =  15,000x + 0

y  =  15,000x

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