Writing linear equations from a table worksheet answer key

Use this sixth-grade math worksheeet to help students learn to recognize addition and multiplication patterns in tables and use them to write simple linear equations based on those patterns. As an added challenge, learners will then need to use the equations they write in order to find missing values in tables. This worksheet is a great way to give students a solid foundation in writing linear equations from tables, which they will encounter again in algebra and beyond.

Grade

Subject

View aligned standards

We can use the information from a table to write the linear equation that represents a given situation without drawing the graph.

Example 1 :

The table shows the temperature of a fish tank during an experiment. Write the appropriate linear equation to find the temperature at any time.

Solution :

Step 1 :

Notice that the change in the temperature is the same for each increase of 1 hour in time. So, the relationship is linear.

Step 2 :

Let x stand for time and y stand for temperature. 

Choose any two points in the form (x, y), from the table 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 3 : 

Find the y-intercept using the slope and any point from the table.

Slope-intercept form equation of a line :

y  =  mx + b

Substitute  m = -2, and (x, y) = (0, 82).

82  =  -2(0) + b

82  =  0 + b

82  =  b

Step 4 : 

Now, substitute m = -2 and b = 82 in slope-intercept form equation of a line.

y  =  mx + b

y  =  -2x + 82

Example 2 :

Elizabeth’s cell phone plan lets her choose how many minutes are included each month. The table shows the plan’s monthly cost y for a given number of included minutes x. Write an equation in slope-intercept form to represent the situation.

Solution :

Step 1 :

Notice that the change in cost is the same for each increase of 100 minutes. So, the relationship is linear.

Step 2 : 

Choose any two points in the form (x, y), from the table to find the slope :

For example, let us choose (100, 14) and (200, 20).

Use the slope formula. 

m  =  (y2 - y1) / (x2 - x1)

Substitute : 

(x1, y1)  =  (100, 14)

(x2, y2)  =  (200, 20)

Then,

m  =  (20 - 14) / (200 - 100)

m  =  6 / 100

m  =  0.06

Step 3 : 

Find the y-intercept using the slope and any point from the table.

Slope-intercept form equation of a line :

y  =  mx + b

Substitute  m  =  0.06, and (x, y)  =  (100, 14).

14  =  0.06(100) + b

14  =  6 + b

8  =  b

Step 4 : 

Now, substitute m = 0.06 and b = 8 in slope-intercept form equation of a line.

y  =  mx + b

y  =  0.06x + 8

Example 3 : 

A salesperson receives a weekly salary plus a commission for each computer sold. The table shows the total pay, y, and the number of computers sold, x. Write an equation in slope-intercept form to represent this situation.

Solution :

Step 1 :

Notice that the change in total pay is the same for increase in sales of every 2 computers. So, the relationship is linear.

Step 2 :

Choose any two points in the form (x, y), from the table to find the slope :

For example, let us choose (4, 550) and (6, 700).

Use the slope formula. 

m  =  (y2 - y1) / (x2 - x1)

Substitute : 

(x1, y1)  =  (4, 550)

(x2, y2)  =  (6, 700)

Then, 

m  =  (700 - 550) / (6 - 4)

m  =  150 / 2

m  =  75

Step 3 : 

Find the y-intercept using the slope and any point from the table.

Slope-intercept form equation of a line :

y  =  mx + b

Substitute m  =  75, and (x, y)  =  (4, 550).

550  =  75(4) + b

550  =  300 + b

250  =  b

Step 4 : 

Now, substitute m = 75 and b = 250 in slope-intercept form equation of a line.

y  =  mx + b

y  =  75x + 250

Kindly mail your feedback to 

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

What is a linear equation worksheet?

How do you write an equation of a line given two points?