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 constan rate of change.
b. a linear proporti equation has a constan of proportionality.
c. the graph of a linear equation is always a line.
d. the graph of a equation goes through the .
e. if a linear equation models a relationship, then the constant is .
f. if a linear equation models a relationship, then it has a of x and a
that is not equal to zero.
word bank: constant, linear, non - linear, proportional, non - proportional, graph, curved, coefficient, zero, straight, origin, function

Explanation:

Step1: Analyze Sentence A

A linear equation has a constant rate of change, so "constant" fits here.

Step2: Analyze Sentence B

A linear proportional equation has a constant of proportionality, so "proportional" and "constant" fit.

Step3: Analyze Sentence C

The graph of a linear equation is a straight line, so "linear" and "straight" fit.

Step4: Analyze Sentence D

The graph of a proportional equation goes through the origin, so "proportional" and "origin" fit.

Step5: Analyze Sentence E

If a linear equation models a proportional relationship, the constant is zero? Wait, no—wait, proportional relationships have constant of proportionality (non - zero), but if it's proportional, and the equation is \(y = kx\), when \(x = 0\), \(y=0\), but the constant (rate of change) is non - zero. Wait, maybe I messed up. Wait, the word bank has "proportional", "constant", "origin", etc. Let's re - do:

Sentence D: The graph of a proportional equation goes through the origin. So first blank: proportional, second blank: origin.

Sentence E: If a linear equation models a proportional relationship, then the constant (of proportionality) is non - zero? Wait, no, the word bank has "zero"? Wait, maybe the intended is: If a linear equation models a proportional relationship, then the constant (y - intercept) is zero. Because proportional equations are \(y=kx\) (y - intercept zero), non - proportional are \(y = kx + b\), \(b
eq0\). So Sentence E: first blank: proportional, second blank: zero.

Sentence F: If a linear equation models a non - proportional relationship, then it has a coefficient of x and a constant (y - intercept) that is not equal to zero. So first blank: non - proportional, second blank: coefficient, third blank: constant.

Now let's fill all:

A. The table of values of a linear equation has a \(\boldsymbol{constant}\) rate of change.

B. A linear \(\boldsymbol{proportional}\) equation has a \(\boldsymbol{constant}\) of proportionality.

C. The graph of a \(\boldsymbol{linear}\) equation is always a \(\boldsymbol{straight}\) line.

D. The graph of a \(\boldsymbol{proportional}\) equation goes through the \(\boldsymbol{origin}\).

E. If a linear equation models a \(\boldsymbol{proportional}\) relationship, then the constant is \(\boldsymbol{zero}\).

F. If a linear equation models a \(\boldsymbol{non - proportional}\) relationship, then it has a \(\boldsymbol{coefficient}\) of x and a \(\boldsymbol{constant}\) 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