The general equation is y = mx + b
The slope of the graph is constant and can be defined as rise over run.
Which of the statements below are true for linear functions? Select all that apply.
The general equation is y = mx + b
The general equation is y = ax^2 + bx + c
The general equation is y = ab^x
The graph contains a vertex.
The slope of the graph is constant and can be defined as rise over run.
3 answers
explain
In a linear function, the general equation is of the form y = mx + b, where m is the slope of the line and b is the y-intercept. This equation describes a straight line graph. The slope of the graph is constant, meaning that it does not change as you move along the line. The slope can be calculated as the rise over run, which is the change in y divided by the change in x as you move between two points on the line.
On the other hand, the equation y = ax^2 + bx + c represents a quadratic function, not a linear function. In a quadratic function, the graph contains a vertex and the relationship between the variables is not linear.
Therefore, the statements that are true for linear functions are:
- The general equation is y = mx + b
- The slope of the graph is constant and can be defined as rise over run.
On the other hand, the equation y = ax^2 + bx + c represents a quadratic function, not a linear function. In a quadratic function, the graph contains a vertex and the relationship between the variables is not linear.
Therefore, the statements that are true for linear functions are:
- The general equation is y = mx + b
- The slope of the graph is constant and can be defined as rise over run.
1 answer