Name: ______________________________________________
MIF 8 Chapter 3 Section 3
Date: ____________________
Representing a relationship between two variables using a linear equation
Equations can also have more than one variable. The table below shows the ages of
Dorothy and her brother Benjamin.
What is the pattern?
If we let Benjamin’s age be _______ and Dorothy’s age be _____ then we can write a
linear equation describing the relationship: ___________________________.
Express a linear equation in two variables
1. Write a linear equation for the relationship between hours, h, and minutes, m.
*hint…think how many minutes are in an hour?
2. Mrs. Ford heated a liquid and
measured its temperature. She
recorded the results in the table at the
right. Write a linear equation for the
relationship between the time, t, and the
liquid’s temperature, T.
*hint…what is the initial temperature? How does the temperature change over time
form there?
3. Write a linear equation for the relationship between days, d, and weeks, w.
*hint…look back at number 1
4. George rented a
car for a week. The
table shows rental
charges.
Write a linear equation for the charge, C, in terms of distance traveled, d.
*hint…look back at number 2
Evaluate linear equations with two variables
If you are given a value for one variable in a linear equation, you can solve for the
other.
Find the value of x in each linear equation if 𝑦 = 7.
1. 𝑦 =
𝑥−5
2
2. 3𝑦 + 4 = 2𝑥
9
3. 𝑥 = 2 𝑦 − 15.5
Find the value of y in each linear equation if 𝑥 = −4.
1. 𝑦 = 7 + 3𝑥
2. −6𝑥 − 𝑦 = 17.75
3.
1
3
1
𝑦 = 2(𝑥 − 6)
Writing tables of values for linear equations with two variables
There are infinitely many pairs of solutions for the two variables in a linear
equation. One way to express some of them is in an organized table.
𝑦
3
Create a table of values for the equation 2 = 2 𝑥 + 2 using integers -1, 0 and 1 for x.
𝑥 = −1
𝑦
𝑥=0
3
𝑦
= 2𝑥 + 2
2
𝑥=1
3
𝑦
= 2𝑥 + 2
2
x
y
-1
3
= 2𝑥 + 2
2
0
1
More Practice
1. Create a table of values for the equation 4𝑦 − 11𝑥 = 6 using integers 1, 2 and 3
for x.
𝑥=1
𝑥=2
4𝑦 − 11𝑥 = 6
𝑥=3
4𝑦 − 11𝑥 = 6
x
4𝑦 − 11𝑥 = 6
1
2
3
y
2. Complete the table of values for the equation
x
y
?
-1
𝑦−2
0
?
3
=𝑥
1
?