PROBLEMS ON WRITING A TABLE FROM LINEAR EQUATIONS FROM TABLE

From the table given below, find the following.

1)  What is the rate?

2)  What is the starting value?

3)  Write the equation:

Problem 1 :

Solution:

Rate (m):

Rate m = (y₂ - y₁)/(x₂ - x₁)

= (7 - 3)/(1 - 0)

m = 4

Starting point (b):

The starting value is the value of y when x = 0. In this case, it is 3 which corresponds to the first data point.

Equation:

y = mx + b

y = 4x + 3

Problem 2 :

Solution:

Rate (m):

Rate m = (y₂ - y₁)/(x₂ - x₁)

= (28 - 30)/(1 - 0)

m = -2

Starting point (b):

The starting value is the value of y when x = 0. In this case, it is 30 which corresponds to the first data point.

Equation:

y = mx + b

y = -2x + 30

Problem 3 :

Solution:

Rate (m):

Rate m = (y₂ - y₁)/(x₂ - x₁)

= (-2 + 4)/(1 - 0)

m = 2

Starting point (b):

The starting value is the value of y when x = 0. In this case, it is -4 which corresponds to the first data point.

Equation:

y = 2x + b

y = -2x - 4

Problem 4 :

Solution:

Rate (m):

Rate m = (y₂ - y₁)/(x₂ - x₁)

= (6 - 0)/(1 - 0)

m = 6

Starting point (b):

The starting value is the value of y when x = 0. In this case, it is 0 which corresponds to the first data point.

Equation:

y = 6x + 0

y = 6x

Problem 5 :

1)  What is the rate?

2)  What is the starting value?

3)  From the equation given, find the missing outputs.

y = 6x - 2

Solution:

1)  Rate (m):

y = 6x - 2

Comparing the linear function with y = mx + b

Rate of change (m) = 6

2)  Starting point (b):

The starting value is the value of y when x = 0.

y = 6x - 2

If x = 0, y = 6(0) - 2 = -2

In this case, it is -2 which corresponds to the first data point.

3)  Missing outputs :

If x = 1, y = 6(1) - 2 = 4

If x = 2, y = 6(2) - 2 = 10

If x = 3, y = 6(3) - 2 = 16

Problem 6 :

1)  What is the rate?

2)  What is the starting value?

3)  From the equation given, find the missing outputs.

y = 2x + 3

Solution:

Rate (m):

y = 2x + 3

Comparing the linear function with y = mx + b

m = 2

Starting point (b):

The starting value is the value of y when x = 0.

If x = 0, y = 2(0) + 3 = 3

In this case, it is 3 which corresponds to the first data point.

3)  Missing outputs :

If x = 1, y = 2(1) + 3 = 5

If x = 2, y = 2(2) + 3 = 7

If x = 3, y = 2(3) + 3 = 9

Problem 7 :

1) What is the rate?

2)  What is the starting value?

3)  From the equation given, find the missing outputs.

y = -5x + 28

Solution:

Rate (m):

y = -5x + 28

Comparing the equation with y = mx + b

m = -5

Starting point (b):

The starting value is the value of y when x = 0.

y = -5x + 28

If x = 0, y = -5(0) + 28 = 28

In this case, it is 28 which corresponds to the first data point. 

3) Missing outputs :

If x = 1, y = -5(1) + 28 = 23

If x = 2, y = -5(2) + 28 = 18

If x = 3, y = -5(3) + 28 = 13

Problem 8 :

1)  What is the rate?

2) What is the starting value?

3)  From the equation given, find the missing outputs.

y = 3x

Solution:

Rate (m):

y = 3x

m = 3

Starting point (b):

The starting value is the value of y when x = 0.

If x = 0, y = 3(0) = 0

In this case, it is 0 which corresponds to the first data point.

3) Missing outputs :

If x = 1, y = 3(1) = 3

If x = 2, y = 3(2) = 6

If x = 3, y = 3(3) = 9