Question

for each table, graph and equation, select whether it is linear and whether it is a function
(y+7) = 3 (x-2)
time temperature
3 5
6 0
9 -5
12 -10

Answer 1

The given equation is: (y+7) = 3(x-2)

To determine whether the equation is linear, we need to check if the highest power of the variable (in this case, y or x) is 1.

In the given equation, if we simplify it, we get y + 7 = 3x - 6. Simplifying further, we get y = 3x - 13.

Since the highest power of the variable is 1 (x), the equation is linear.


Now, let's determine whether it is a function.

Since the equation can be simplified to y = 3x - 13, we can see that for each value of x, there is a unique corresponding value of y. Therefore, the equation represents a function.


Time Temperature
3 5
6 0
9 -5
12 -10

To determine whether the table represents a linear relation, we need to check if the difference in the y-values (temperature) is constant for each difference in x-values (time).

In this case, the difference in the y-values between each consecutive pair of x-values is -5. Therefore, the table represents a linear relation.

Additionally, since there is only one y-value for each x-value in the table, it represents a function.


In summary:

Equation: Linear and Function
Table: Linear and Function