Question

Do these ordered pairs satisfy a linear function? Explain. {(0,1),(1,2),(2,4),(3,8),(4,16)}

Answer 1

Yes, these ordered pairs satisfy a linear function with a consistent slope. The slope is calculated between each pair of points and is the same for all pairs, indicating a linear relationship.

Step-by-step explanation:

Yes, these ordered pairs satisfy a linear function. A linear function is a function where the equation can be written in the form y = mx + b, where m and b are constants.

To check if the given ordered pairs satisfy a linear function, we can calculate the slope (m) between each pair of points. If the slope is the same for all pairs, then the function is linear.

Let's calculate the slopes:

1. 
   
2. Between (0,1) and (1,2): m = (2 - 1)/(1 - 0) = 1/1 = 1
3. 
   
4. Between (1,2) and (2,4): m = (4 - 2)/(2 - 1) = 2/1 = 2
5. 
   
6. Between (2,4) and (3,8): m = (8 - 4)/(3 - 2) = 4/1 = 4
7. 
   
8. Between (3,8) and (4,16): m = (16 - 8)/(4 - 3) = 8/1 = 8
9. 
   

Since the slope is the same (1, 2, 4, 8) for all pairs, the ordered pairs satisfy a linear function. Therefore, the function can be represented as y = mx + b, where m = 1 and b is the y-intercept.

Answer 2

You must look at the slopes to determine whether or not it is a linear function. A linear funtion has a constant slope. So, the slope must be the same throughout the entire function. You would need to use the formula m=(y2-y1)/(x2-x1) to find the slope beween different points that were given. Basically, any inconsistency indicates that it is not a linear function; those coordinates cannot be classified as being a linear function due to the fact that the slope is not constant throughout the function.