Question

Write the linear equation that gives the rule for this table.

f(x) | A | 1 | 5 | N | 6 | 3 | 4 | 7
a) f(x) = 4x - 3
b) f(x) = 5x + 1
c) f(x) = 3x + 2
d) f(x) = 7x - 1

Answer 1

The linear equation that describes the table is f(x) = 3x + 2.

Step-by-step explanation:

The linear equation that gives the rule for the table is f(x) = 3x + 2.

To determine the equation, we can look at the pattern in the table. As the values of x increase by 1, the values of y increase by 3. This indicates a slope of 3. Additionally, when x is 1, y is 5. This gives us the y-intercept of 2. Therefore, the equation is f(x) = 3x + 2.

Example:
For x = 4, f(x) = 3(4) + 2 = 14.