Question

The data in the table below satisfies a linear equation.

n c
-7 -16
-6 -13
3 14
5 20
9 32
a
c = n +15
b
c = 4n - 4
c
c = 2n -1
d
c = 3n + 5

Answer 1

The given data represents a linear equation, and the equation that satisfies all the given points is c = 3n + 5.

Step-by-step explanation:

The given data represents a linear equation. To determine which equation best represents the data, we can check whether the equation satisfies all the given points. Let's check each equation:

a) c = n + 15:

For n = -7, c = -7 + 15 = 8 (correct)

For n = -6, c = -6 + 15 = 9 (incorrect)

For n = 3, c = 3 + 15 = 18 (incorrect)

For n = 5, c = 5 + 15 = 20 (correct)

For n = 9, c = 9 + 15 = 24 (incorrect)

The equation does not satisfy all the given points.

b) c = 4n - 4:

For n = -7, c = 4(-7) - 4 = -32 (incorrect)

For n = -6, c = 4(-6) - 4 = -28 (incorrect)

For n = 3, c = 4(3) - 4 = 8 (incorrect)

For n = 5, c = 4(5) - 4 = 16 (incorrect)

For n = 9, c = 4(9) - 4 = 32 (correct)

The equation does not satisfy all the given points.

c) c = 2n - 1:

For n = -7, c = 2(-7) - 1 = -15 (incorrect)

For n = -6, c = 2(-6) - 1 = -13 (correct)

For n = 3, c = 2(3) - 1 = 5 (incorrect)

For n = 5, c = 2(5) - 1 = 9 (incorrect)

For n = 9, c = 2(9) - 1 = 17 (incorrect)

The equation does not satisfy all the given points.

d) c = 3n + 5:

For n = -7, c = 3(-7) + 5 = -16 (correct)

For n = -6, c = 3(-6) + 5 = -13 (correct)

For n = 3, c = 3(3) + 5 = 14 (correct)

For n = 5, c = 3(5) + 5 = 20 (correct)

For n = 9, c = 3(9) + 5 = 32 (correct)

The equation satisfies all the given points.

Therefore, the correct equation that represents the data is c = 3n + 5.

Answer 2

c = 3n + 5

Step-by-step explanation:

The equation c = 3n + 5 fits the data in the table. When n = -7, c = -7 * 3 + 5 = -16. When n = -6, c = -6 * 3 + 5 = -13. When n = 3, c = 3 * 3 + 5 = 14. When n = 5, c = 5 * 3 + 5 = 20. And when n = 9, c = 9 * 3 + 5 = 32. All the values of c in the table match the values predicted by the equation c = 3n + 5. Therefore, c = 3n + 5 is the correct equation for the data.