Question

1. use the terms in the word bank to complete the sentences below. some terms may be used more than once, and some may not be used at all.

a. the table of values of a linear equation has a
ate of change.
b. a linear equation has a of proportionality.
c. the graph of a equation is always a line.
d. the graph of a equation goes through the .
e. if a linear equation models a
elationship, then the constant is .
f. if a linear equation models a
elationship, then it has a of x and a \that is not equal to zero.

word bank: a constant, a linear, a non - linear, a proportional, a non - proportional, a graph, a curved, a coefficient, a zero, a straight, a origin

Explanation:

Step1: Analyze Part A

A linear equation has a constant rate of change. So for "The table of values of a linear equation has a [ ] rate of change", the term is "constant".

Step2: Analyze Part B

A linear proportional equation has a constant of proportionality. So "A linear [proportional] equation has a [constant] of proportionality".

Step3: Analyze Part C

The graph of a linear equation is always a straight line. So "The graph of a [linear] equation is always a [straight] line".

Step4: Analyze Part D

The graph of a proportional (linear proportional) equation goes through the origin. So "The graph of a [proportional] equation goes through the [origin]".

Step5: Analyze Part E

If a linear equation models a proportional relationship, the constant is zero (since \(y = kx\), when \(x = 0\), \(y = 0\)). So "If a linear equation models a [proportional] relationship, then the constant is [zero]".

Step6: Analyze Part F

If a linear equation models a non - proportional relationship, it has a coefficient of \(x\) and a constant that is not zero (e.g., \(y=mx + b\), \(b
eq0\)). So "If a linear equation models a [non - proportional] relationship, then it has a [coefficient] of \(x\) and a [constant] that is not equal to zero".

Answer:

A. constant
B. proportional, constant
C. linear, straight
D. proportional, origin
E. proportional, zero
F. non - proportional, coefficient, constant