**Writing linear equations from word problems worksheet :**

Worksheet on writing linear equations from word problems is much useful to the students who would like to practice solving real world problems on linear equations.

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.

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.

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.

**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.

**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 (0, 82) for (x₁, y₁) and (1, 80) for (x₂, y₂).

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

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

82 = -2(0) + b

82 = 0 + b

82 = b

**Step 4 : **

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

y = mx + b

y = -2x + 82

**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.

**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 (100, 14) for (x₁, y₁) and (200, 20) for (x₂, y₂).

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

Plug m = 0.06, and (x, y) = (100, 14)

14 = 0.06(100) + b

14 = 6 + b

8 = b

**Step 4 : **

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

y = mx + b

y = 0.06x + 8

**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.

**Solution : **

**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 (600, 750) for (x₁, y₁) and (900, 1150) for (x₂, y₂).

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

Plug 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

y = mx + b

Plug m = 4/3 and b = -50

y = (4/3)x + (-50)

y = (4/3)x - 50

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