Question

1. determine if the functions are linear or nonlinear.

a. y = 8x + 3
b. y = 3x^2 - x + 3
c. y = -\frac{3}{7}x+\frac{5}{2}
linear nonlinear
linear nonlinear
linear nonlinear

Explanation:

Step1: Recall linear - function form

A linear function is of the form $y = mx + b$, where $m$ and $b$ are constants and the highest power of $x$ is 1.

Step2: Analyze function a

For $y = 8x+3$, it is in the form $y = mx + b$ with $m = 8$ and $b = 3$. So it is linear.

Step3: Analyze function b

For $y=3x^{2}-x + 3$, the highest - power of $x$ is 2. So it is nonlinear.

Step4: Analyze function c

For $y=-\frac{3}{7}x+\frac{5}{2}$, it is in the form $y = mx + b$ with $m=-\frac{3}{7}$ and $b=\frac{5}{2}$. So it is linear.

Answer:

a. LINEAR
b. NONLINEAR
c. LINEAR