Question

2. Calculate the rate of change for the following linear functions.

Answer 1

Formula to find the slope, m, or change in function of a graph is given below as,

`m=(y_2-y_1)/(x_2-x_1)`

For the first linear graph,

`\begin{gathered} \text{Where x = 0, y = 0 }_{} \\ (x_1,y_1)=(0,0) \\ \text{Where }x\text{ = -2, y = 2} \\ (x_2,y_2)=(-2,2) \end{gathered}`

Substituting the coordinates into the equation,

`m=(2-0)/(-2-0)=(2)/(-2)=-1`

For the second linear graph,

`\begin{gathered} \text{Where x = 0, y = 2} \\ (x_1,y_1)=(0,2) \\ \text{Where x = 2, y = 2} \\ (x_2,y_2)=(2,2) \end{gathered}`

Substituting the coordinates into the equation,

`m=(2-2)/(2-0)=(0)/(2)=0`

For the third linear graph,

`\begin{gathered} \text{Where x = -4, y = 0} \\ (x_1,y_1)=(-4,0) \\ \text{Where x = -4, y = 2} \\ (x_(2,)y_2)=(-4,2) \end{gathered}`

Substituting the coordinates into the equation,

`m=(2-0)/(-4-(-4))=(2)/(-4+4)=(2)/(0)=\infty`

Hence, the slope of the first graph is -1.

Slope of the second graph is 0 since it doesn't rise vertically.

Slope of the third graph is infinite because it is a vertical line that neither move to the left or right.