We can write a linear equation for the information found in the given real-world problem and solve the problem using the linear equation.

In most of the cases, we use slope-intercept form equation to solve the real-world problems.

**Problem 1 : **

The table shows the temperature of a fish tank during an experiment. Write the appropriate linear equation for the given situation and use the equation to find temperature at the 7th hour. .

**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.

Since we want to find the temperature at the 7th hour, the appropriate linear equation for the given situation is slope-intercept form (y = mx + b), assuming "y" as temperature and "x" as hours.

**Step 2 : **

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 = (y_{2} - y_{1}) / (x_{2} - x_{1})

Substitute (0, 82) for (x_{1}, y_{1}) and (1, 80) for (x_{2}, y_{2}).

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

**Step 5 : **

Find the temperature at the 7th hour.

Plug x = 7 in the equation y = -2x + 82.

y = -2(7) + 82

y = -14 + 82

y = 68

So, the temperature at the 7th hour is 68⁰ F.

**Problem 2 : **

Lily has just opened her new computer store. She makes $25 on every computer she sells and her monthly expenses are $10,000. What is the minimum number of computer does she need to sell in a month to make a profit ?

**Solution : **

**Step 1 : **

Let "y" stand for the profit and "x' stand for number of computers sold.

From the given information, we have

Profit = 27 x No. of computers sold - Monthly expenses

y = 27x -10,000

**Step 2 : **

Let us find the number of computers sold for no profit.

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

Plug y = 0 in the equation y = 27x - 10,000.

0 = 25x - 10,000

Add 10,000 to both sides.

10,000 = 25x

Divide both sides by 25.

10,000 / 25 = 25x / 25

400 = x

**Step 3 : **

When Lily sells 400 computers in a month, her profit is equal to zero.

So, she has to sell more than 400 computer per month to make a profit.

To make a profit, the minimum number of computers per month, she needs to sell is 401.

**Problem 3 : **

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 and use it to estimate cost of plan for 800 minutes included.

**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 = (y_{2} - y_{1}) / (x_{2} - x_{1})

Substitute (100, 14) for (x_{1}, y_{1}) and (200, 20) for (x_{2}, y_{2}).

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

**Step 5 : **

Estimate cost of plan for 800 minutes included.

Plug x = 800 in the equation y = 0.06x + 8.

y = 0.06(800) + 8

y = 48 + 8

y = 56

So, the cost of plan for 800 minutes included is $56.

**Problem 4 : **

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 and use it to calculate the rent for 1200 square feet of space.

**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 = (y_{2} - y_{1}) / (x_{2} - x_{1})

Substitute (600, 750) for (x_{1}, y_{1}) and (900, 1150) for (x_{2}, y_{2}).

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

**Step 6 : **

Calculate the rent for 1200 square feet of space.

Plug x = 1200 in the equation y = (4/3)x - 50.

y = (4/3)(1200) - 50

y = 1600 - 50

y = 1550

So, the rent for 1200 square feet of space is $1550.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit the following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**