. Which graph best represents a first-degree polynomial p(x)?
since a first degree polynomial is
y = mx+b
does that look familiar?
To determine the graph that best represents a first-degree polynomial, it is essential to understand what a first-degree polynomial is first. A first-degree polynomial, also known as a linear function, is a polynomial of degree 1, meaning it consists of terms with a maximum exponent of 1.
The general form of a first-degree polynomial is:
p(x) = ax + b
where a and b are constants.
For a first-degree polynomial, the graph is always a straight line because the highest power of x is 1. The slope of the line is given by the coefficient 'a' in the equation, and 'b' represents the y-intercept, which is the point where the line intersects the y-axis.
To determine the best graph that represents a first-degree polynomial p(x), consider the following characteristics:
1. Slope: The slope determines whether the line rises or falls and how steeply it does so. If 'a' is positive, the line will rise from left to right, whereas if 'a' is negative, the line will fall from left to right.
2. Y-Intercept: The y-intercept is the point where the line intersects the y-axis. It is represented by the constant 'b' in the equation. The y-intercept determines the vertical position of the line.
Based on these characteristics, the graph that best represents a first-degree polynomial p(x) will be a straight line either rising or falling, depending on the value of 'a', with a y-intercept determined by 'b'.
Unfortunately, I cannot provide visual representation here, but you can plot the graph of a first-degree polynomial using software or online graphing tools like Desmos, GeoGebra, or Graphing Calculator. Simply input the equation p(x) = ax + b, assign suitable values to 'a' and 'b,' and plot the resulting line to visualize the graph.
Remember, adjusting values of 'a' and 'b' will give you different lines, representing different first-degree polynomials.