Compare Linear Functions and example
Rate of change:
y-intercept:
Linear Functions:
- Linear functions have a constant rate of change, which means that the change in the y-values is constant for each unit increase in the x-values.
- The equation for a linear function is in the form of y = mx + b, where m represents the slope or rate of change and b represents the y-intercept.
- The graph of a linear function is a straight line.
- Example: y = 2x + 3 represents a linear function. The rate of change is 2, which means for every unit increase in x, y will increase by 2. The y-intercept is 3, indicating that the line crosses the y-axis at the point (0, 3).
y-intercept:
- The y-intercept of a linear function is the point where the graph intersects the y-axis.
- It is the value of y when x is 0.
- The y-intercept is represented by the value of b in the equation y = mx + b.
- Example: In the linear function y = 2x + 3, the y-intercept is 3, indicating that the graph crosses the y-axis at the point (0, 3). This means that when x is 0, y is equal to 3.
Compare Linear Functions Rate of change: and y-intercept: and add an example for both Rate of change nd y-intercept
Rate of change:
- Linear functions have a constant rate of change, which means that the change in the y-values is constant for each unit increase in the x-values.
- The rate of change is represented by the slope of the linear function and is denoted by the variable m in the equation y = mx + b.
- The rate of change determines how steep or flat the line is on the graph.
- Example: Consider the linear function y = 2x + 3. Here, the rate of change is 2, indicating that for every unit increase in x, y increases by 2. So if x increases from 1 to 2, y will increase from 5 to 7.
y-intercept:
- The y-intercept of a linear function is the point where the graph intersects the y-axis.
- It represents the value of y when x is equal to 0.
- The y-intercept is denoted by the variable b in the equation y = mx + b.
- Example: In the linear function y = 2x + 3, the y-intercept is 3. This means that when x is 0, y is equal to 3. So the line crosses the y-axis at the point (0, 3).