Final answer:
The algebraic expression (3x^3 + 2y + 4) has variables x and y, coefficients 3 and 2, and the constant 4. Learning to graph polynomials involves understanding how these terms affect the shape of the curve. In linear equations like y = 9 + 3x, x is the independent variable, y is dependent, the y-intercept is 9, and the slope is 3, detailing the relationship and graph of the function.
Step-by-step explanation:
The given algebraic expression is (3x^3 + 2y + 4).
- The variables in the expression are x and y.
- The coefficients are the numerical multipliers of the variables, which are 3 for the term 3x^3 and 2 for the term 2y.
- The constant is a term in the expression that does not contain any variables, which is 4.
If we were to graph a polynomial like this, the shape of the curve changes as the constants are adjusted. When you learn about graphing polynomials, you'd observe how the individual terms like y = bx contribute to the overall shape of the polynomial curve.
Consider a different, simpler equation, y = 9 + 3x, which represents a straight line. In this case:
- x is the independent variable since its value is chosen freely.
- y is the dependent variable because its value depends on the value chosen for x.
- The y-intercept of this line is 9 since that's the value of y when x is 0 (the point where the line crosses the y-axis).
- The slope of the line is 3, which indicates the steepness of the line and is calculated as the rise over the run between two points on the line.
You would construct a table to show the values of x and y, plot these values on a graph, and then draw the line through them to visually represent the equation.