Question

[x] [y]

[0] [2]
[unknown] [11/3]
[3] [7]
[5] [31/3]
[8] [unknown]

The table represents a linear function. Find the missing values to complete the table.
A) x = 1, y = 41/3
B) x = 1, y = 46/3
C) x = 2, y = 41/3
D) x = 2, y = 46/3

Answer 1

x = 1, y = 46\3

y-intercept = 2

slope(m) =

7 - 2 \3 - 0 = 5 \3

thus,

y = 5 \3 x + 2

then, plug in values

Answer 2

B) x = 1, y = 46/3

Explanation:

The general equation for a straight line is

y = mx + b

Step 1. Find the slope of the line

The slope m is

m =(y₂ -y₁)/(x₂/x₁)

Two of your points are (0, 2) and (3, 7).

m = (7 – 2)/(3 – 0)

m = 5/3

Step 2. Find the equation of the line

Use point (0, 2).

2 = ⁵/₃ × 0 + b

2 = 0 + b

b = 2

The equation of the line is

y = ⁵/₃x + 2

===============

Step 3.Find the coordinates of the first missing point.

(x, 11/3)

11/3 = ⁵/₃x + 2 Multiply each side by 3

11 = 5x + 6 Subtract 6 from each side

5 = 5x Divide each side by 5

x = 1

The missing value is x = 1.

===============

Step 4. Find the coordinates of the second missing point

(8, y)

y = ⁵/₃ × 8 + 2 Multiply each side by 3

3y = 40 + 6 Combine like terms

3y = 46 Divide each side by 3

y = 46/3

The missing value is y = 46/3.

Your three known points give the green line in the graph below.

The orange dot represents the first missing point at (1, 11/3).

The red dot represents the second missing point at (8, 46/3).