Question

 Two different functions are represented by this graph and this table:

Answer 1

Option B is correct.

Function B has the greater slope.

3 is greater than 2.

Step-by-step explanation

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

`Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=(y_2-y_1)/(x_2-x_1)`

For function A, we will pick two points on the line

(x₁, y₁) and (x₂, y₂) are (-2, -1) and (0, 3)

`\text{Slope = }(3-(-1))/(0-(-2))=(3+1)/(0+2)=(4)/(2)=2`

For function B, we will pick the two most extreme points on the table

(x₁, y₁) and (x₂, y₂) are (0, 1) and (5, 16)

`\text{Slope = }(16-1)/(5-0)=(15)/(5)=3`

We can easily see that function B (3) has a greater slope than function A (2).

Hope this Helps!!!