The graph represents function 1 and the equation represents function 2:
A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3.
Function 2
y = 4x + 1
How much more is the rate of change of function 2 than the rate of change of function 1?
To determine the rate of change of each function, we need to find the slope of the lines representing each function.
For function 1, the graph shows a horizontal straight line joining the points (0, 3) and (4, 3). Since the y-coordinate remains constant, the slope is 0 because there is no change in the y-values as x increases. Thus, the rate of change of function 1 is 0.
For function 2, the equation y = 4x + 1 represents a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept. The slope (rate of change) for function 2 is 4 because the coefficient of x is 4. Therefore, the rate of change of function 2 is 4.
To find how much more the rate of change of function 2 is than the rate of change of function 1, we subtract the rate of change of function 1 from the rate of change of function 2:
4 - 0 = 4
Hence, the rate of change of function 2 is 4 units more than the rate of change of function 1.
To determine the rate of change of a function, we need to look at the slope of the graph or the coefficient of the variable in the equation.
For function 1, we have a horizontal straight line with a constant y-value of 3. Since the line is horizontal, the slope is 0, which means the rate of change is 0.
For function 2, we have the equation y = 4x + 1. The coefficient of the x-term is 4, which represents the rate of change.
Therefore, the rate of change of function 1 is 0, and the rate of change of function 2 is 4.
To find out how much more the rate of change of function 2 is than the rate of change of function 1, we simply subtract the two values:
4 - 0 = 4
Therefore, the rate of change of function 2 is 4 units greater than the rate of change of function 1.
horizontal lines have zero slope, so rate of change (=slope)=0.
Any straight-line function has the form
y=mx+b
where m is the slope, and b is a constant.
Compare this with the equation of function 2 to determine the slope.
Since rate of change of function 1 is zero, so function 2's rate of change is m-0=m.