Question

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 = 2x + 1
How much more is the rate of change of function 2 than the rate of change of function 1?

Answer 1

Answer:

The rate of change of function 1 is 0 and the rate of change of function 2 is 2. The rate of change of function 2 is 2 more than the rate of change of function 1.

Step-by-step explanation:

The rate of change is also known as slope. The slope of a linear function or a line is

$m=\frac{y_2-y_1}{x_2-x_1}$

It is given that the function 1 is passing through the points (0,3) and (4,3). Slope of function 1 is

$m_1=\frac{3-3}{4-0}$

$m_1=\frac{0}{4}$

$m_1=0$

Therefore the slope of first function is 0.

The slope intercept form of a line is

$y=mx+b$

Where, m is the slope and b is y-intercept.

The second function is

$y=2x+1$

Therefore the slope of second function is 2 and the y-intercept is 1.

The rate of change of function 1 is 0 and the rate of change of function 2 is 2. The rate of change of function 2 is 2 more than the rate of change of function 1.

Answer 2

There is no rate of change of Function 1.  It's slope(rate of change) is zero.
Function 2 has a slope of 2.