Download U1 L6 Writing Linear Equations

Unit 1: Relationships between Quantities and Reasoning with Equations
Lesson 6- Writing Linear Equations
Objectives:
 I can determine if an equation is linear.
 I can determine how many solutions a linear equation has.
 I can solve real-world problems by writing an equation that
represents the situation and solving it.
Warm Up: Solve.
3x – 5 = 6(x – 1) – 2
𝑦+4
=5
3
Writing Linear Equations:
In linear equations, variables are raised only to the first power. The
equation 12x – 7 = -5 is linear because the variable, x, is raised to the
first power. The equation x2 + 5y = 32 is not linear because the
variable, x, is raised to the second power.
2
2
The equation 𝑦 = is also not linear. Remember that can be
𝑥
𝑥
written as 2(x-1). Since x is raised to a power other than 1, the
equation is not linear.
Create at least one example of a linear equation and a
non-linear equation.
Linear:
Non-linear:
The solution to a linear equation in one variable is the value that,
when substituted into the equation for the variable, results in a true
number statement, such as 1 = 1. Linear equations in one variable
usually have one solution, but some have no solution and others
have an infinite number of solutions.
Remember how to solve equations?
Write the 5 steps you learned to solve an equation.
Let’s take a look at some equations and find the solution.
3(x – 1) + 2 = 4x
3x – 3 = 2x + x + 4
2x – 3 – x = 3x – 2x – 3
4x + 3 = 2(x – 4)
Don’t forget…
To check the solution to a linear equation, apply the substitution
property of equality by substituting the solution for x in the original
equation and then evaluate. If the result is a true number statement,
then your solution is correct. Choose one of the equations above and
check the solution.
Writing Equations:
Many real-world situations can be modeled by using linear equations.
Linear equations can often be used to model situations that involve a
constant rate. For example, a plane flying at a constant speed of 600
mph covers a distance of 600x miles in x hours. The time it takes to
fly 2,000 miles can be found by solving the linear equation
600x = 2,000.
Think…
Make sure the answer makes sense! If you are dealing with time or
distance, can you have a negative answer? If you are finding how
many people there are, do you want partial people? Always look
back at the problem to make sure your answer is appropriate.
Let’s try a few…
A babysitter charges a $10 fee for each job plus $8.50 per hour of
babysitting. How many hours does she need to babysit in order to
buy a new jacket that costs $95 with tax.
Brad is riding his bike at a constant speed from his house to school.
He can ride 12 miles per hour. How long will it take him to get to
school if the trip is 6 miles?
The sum of three consecutive numbers is 18. What are the three
numbers?
The sum of two consecutive even numbers is 110. What are the two
numbers?
You try!
A rectangle’s length is 3 feet longer than its width. Its perimeter is 67
feet. What are the dimensions of the rectangle?
A kitten was born weighing 90 grams and gained 10 grams each day
during the first week. If the kitten continued to gain weight at the
same rate, how long would it take for the kitten to weigh 160 grams?
Find three consecutive numbers whose sum is 156.
====================================================
The sum of 3 consecutive integers is 72. What are the
numbers?
Name: _________________________
Unit 1 Lesson 6: Writing Linear Equations
1) A plumber charges a flat fee of $50 for each job, plus an hourly
rate of $65 per hour for the number of hours the job takes to
complete. Write an equation to represent this situation. If the job
takes 5 hours to complete, how much money will it cost you?
2) The sum of three consecutive integers is 36. What are the
numbers?
3) Bryce is riding his bicycle at a constant speed of 15 mph from
school to the library. It is 10 miles from school to the library. Write an
equation to represent this situation. How long will it take Bryce to get
to the library?
4) A triangle has sides with lengths that are consecutive odd integers.
The perimeter of the triangle is 141 centimeters. Sketch the triangle
and label the lengths of the sides, using the variable a. Then find the
lengths of the sides.
5) Solve. Check your solution if
possible.
6) Solve. Check your solution if
possible.
4x + 2x – 6 = 3(2x – 2)
2(3x + 4) + 6 = 5x + 4
7) Solve. Check your solution if
possible.
8) Solve. Check your solution if
possible.
6x – 5 + 2 = 3(2x + 1)
2x – 4 + 5x = 4(2x – 1)