Given:
Graph of function 1.
The equation of function 2 is [tex]y=\dfrac{1}{2}x+7[/tex].
To find:
The function which has a greater rate of change.
Step-by-step explanation:
From the given graph it is clear that, the function 1 passes through two points (0,0) and (1,2). So, slope of function is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{2-0}{1-0}[/tex]
[tex]m=\dfrac{2}{1}[/tex]
[tex]m=2[/tex]
So, rate of change of function 1 is 2.
On comparing the equation [tex]y=\dfrac{1}{2}x+7[/tex] with [tex]y=mx+b[/tex], where m is slope and b is y-intercept, we get
[tex]m=\dfrac{1}{2}[/tex]
So, rate of change of function 2 is [tex]\dfrac{1}{2}[/tex].
Since, [tex]2>\dfrac{1}{2}[/tex], therefore, function 1 has a greater rate of change.
Solution :
Function 1 passes through (0,0) and (1,2) .
So, equation of function 1 is :
[tex]y - 0 = \dfrac{2-0}{1-0}(x-0)[/tex]
y = 2x
Function 2 is : y = 0.5x + 7
We know coefficient of x in linear equation is the slope.
Also, rate of change is directly proportional to slope.
Therefore, function 1 has a greater rate of change.