To determine if the equation [tex]\( y = 3x + 2 \)[/tex] is linear, quadratic, or exponential, we need to analyze the form of the equation.
1. Linear Equation:
A linear equation in one variable has the form [tex]\( y = mx + c \)[/tex], where [tex]\( m \)[/tex] and [tex]\( c \)[/tex] are constants. The graph of a linear equation is a straight line. In this form, [tex]\( x \)[/tex] is raised to the power of 1.
2. Quadratic Equation:
A quadratic equation in one variable has the form [tex]\( y = ax^2 + bx + c \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants, and [tex]\( a \neq 0 \)[/tex]. The graph of a quadratic equation is a parabola. In this form, [tex]\( x \)[/tex] is raised to the power of 2.
3. Exponential Equation:
An exponential equation has the form [tex]\( y = a \cdot b^x \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants, and [tex]\( b \neq 1 \)[/tex]. The graph of an exponential equation shows exponential growth or decay. In this form, [tex]\( x \)[/tex] is in the exponent.
Given the equation [tex]\( y = 3x + 2 \)[/tex]:
- The equation is of the form [tex]\( y = mx + c \)[/tex], with [tex]\( m = 3 \)[/tex] and [tex]\( c = 2 \)[/tex].
- This matches the form of a linear equation, as both [tex]\( m \)[/tex] and [tex]\( c \)[/tex] are constants, and [tex]\( x \)[/tex] is raised to the power of 1.
Therefore, the equation [tex]\( y = 3x + 2 \)[/tex] is linear.
The correct classification for [tex]\( y = 3x + 2 \)[/tex] is:
- Linear
