WRITE A LINEAR FUNCTION FROM A TABLE

Look for a pattern in the table. Then write an equation that represents the table.

Problem 1 :

Solution :

Let the linear function, y = mx + b -----(1)

If x = 0 and y = 11, y-intercept(b) is 11.

From the table, the points are (1, 15) and (2, 19).

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

m = (19 - 15)/(2 - 1)

m = 4/1

m = 4

By applying the value of m and b, we get

y = 4x + 11

Problem 2 :

Solution :

Let the linear function, y = mx + b -----(1)

If x = 0 and y = 46, y-intercept(b) is 46.

From the table, the points are (1, 36) and (2, 26).

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

m = (26 - 36)/(2 - 1)

m = -10/1

m = -10

By applying the value of m and b, we get

y = -10x + 46

Problem 3 :

Solution :

Let the linear function, y = mx + b -----(1)

If x = 0 and y = 60, y-intercept(b) is 60.

From the table, the points are (1, 45) and (2, 30).

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

m = (30 - 45)/(2 - 1)

m = -15/1

m = -15

By applying the value of m and b, we get

y = -15x + 46

Problem 4 :

Solution :

Let the linear function, y = mx + b -----(1)

If x = 0 and y = 57, y-intercept(b) is 57.

From the table, the points are (1, 107) and (2, 157).

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

m = (157 - 107)/(2 - 1)

m = 50/1

m = 50

By applying the value of m and b, we get

y = 50x + 57

Problem 5 :

Which equation represents the table at the right ?

(a) y = 5x + 7   (b) y = 7x + 5

(c) y = 12x - 5   (d)  y = 7x + 12

Solution :

Let the linear function, y = mx + b -----(1)

If x = 0 and y = 12, y-intercept(b) is 12.

From the table, the points are (1, 19) and (2, 26).

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

m = (26 - 19)/(2 - 1)

m = 7/1

m = 7

By applying the value of m and b, we get

y = 7x + 12

So, option D is correct.

Problem 6 :

The first story of a building is 24 feet high, and each additional story is 18 feet high. Write an expression for the height to the top of the nth story. Explain the meaning of each term in the expression.

Solution :

Height of the building  = 24 feet

Height of each additional story(m) = 18 feet

y = mx + b 

y = 18x + 24