Question

semester 1: unit 4 exam review
possible points: 1
two students are discussing whether an equation with no exponents greater than 1 must be linear.
student a says:
\if there are no exponents greater than 1, then the graph of the equation will always be a straight line.\
student b disagrees and says:
\there are equations with no exponents greater than 1 that are not linear.\
which equation supports student bs argument?
a. $y = 2x - 5$
b. $y = |x - 4|$
c. $x + y = 7$
d. $y - x = 1$
a
b
c
d

Explanation:

Step1: Define linear equation

A linear equation in two variables has the form $Ax + By = C$ (A, B, C constants, A/B not both 0), and its graph is a straight line.

Step2: Analyze Option A

$y=2x-5$ fits $2x - y = 5$, linear.

Step3: Analyze Option B

$y=|x-4|$ can be rewritten as a piecewise function:

$$ y=
LATEXBLOCK0
$$

Its graph is a V-shape (not a single straight line), and it cannot be written in $Ax+By=C$ form. It has no exponents >1, but is non-linear.

Step4: Analyze Option C

$x+y=7$ fits the linear form, linear.

Step5: Analyze Option D

$y-x=1$ fits $-x + y = 1$, linear.

Answer:

B. $y = |x - 4|$