WRITING LINEAR EQUATIONS FROM WORD PROBLEMS WORKSHEET

Problem 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. 

Problem 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.

Problem 3 :

The rent charged for space in an office building is a linear relationship related to the size of the space rented. At west main street office rentals, $750 rent charged for 600 square feet of space and $1150 rent charged for 900 square feet of space. Write an equation in slope-intercept form for the rent at West Main Street Office Rentals.

Answers

1. Answer :

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

2. Answer :

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

3. Answer :

Step 1 :

Identify the independent and dependent variables.

The independent variable (x) is the square footage of floor space.

The dependent variable (y) is the monthly rent.

Step 2 :

Write the information given in the problem as ordered pairs.

The rent for 600 square feet of floor space is $750 :

(600, 750)

The rent for 900 square feet of floor space is $1150 :

(900, 1150)

Step 3 : 

Find the slope.  

m  =  (y₂ - y₁)/(x₂ - x₁)

Substitute : 

(x₁, y₁)  =  (600, 750)

(x₂, y₂)  =  (900, 1150)

Then, 

m  =  (1150 - 750)/(900 - 600)

m  =  400/300

m  =  4/3

Step 4 : 

Find the y-intercept.

Use the slope 4/3 and one of the ordered pairs (600, 750).

Slope-intercept form : 

y  =  mx + b

Substitute m = 4/3,  x = 600 and y = 750.  

750  =  (4/3)(600) + b

750  =  (4)(200) + b

750  =  800 + b

-50  =  b

Step 5 : 

Substitute the slope and y-intercept.

Slope-intercept form equation of a line :

y  =  mx + b 

Substitute m = 4/3 and b = -50.

y  =  (4/3)x + (-50)

y  =  (4/3)x - 50 

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