# GRAPHING FROM A TABLE TO WRITE AN EQUATION

## About "Graphing from a table to write an equation"

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.

## Graphing from a table to write an equation

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 (0, 82) for (x₁, y) and (1, 80) for (x, y₂)

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

Plug 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 (5, 75,000) for (x₁, y) and (10, 150,000) for (x, y₂).

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

Plug m  =  15,000 and b  =  0

y  =  15,000x + 0

y  =  15,000x

After having gone through the stuff given above, we hope that the students would have understood "Graphing from a table to write an equation".

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