Question

first, complete the table of x- and y-coordinates.

x | y
2 |
3 |
4 |

next, which rule describes the relationship between x and y in the graph?
choose 1 answer:
a multiply x by 2. subtract the product from 10 to get y.
b multiply x by 2. add 2 to the product to get y.

Explanation:

Step1: Identify coordinates from graph

From the graph, when \( x = 0 \), \( y = 10 \); \( x = 1 \), \( y = 8 \); \( x = 2 \), \( y = 6 \); \( x = 3 \), \( y = 4 \); \( x = 4 \), \( y = 2 \); \( x = 5 \), \( y = 0 \). So for \( x = 2 \), \( y = 6 \); \( x = 3 \), \( y = 4 \); \( x = 4 \), \( y = 2 \).

Step2: Test option A

Option A: \( y = 10 - 2x \). For \( x = 2 \): \( 10 - 2(2)=6 \) (matches \( y = 6 \)). For \( x = 3 \): \( 10 - 2(3)=4 \) (matches \( y = 4 \)). For \( x = 4 \): \( 10 - 2(4)=2 \) (matches \( y = 2 \)).

Step3: Test option B

Option B: \( y = 2x + 2 \). For \( x = 2 \): \( 2(2)+2 = 6 \) (matches), but \( x = 3 \): \( 2(3)+2 = 8
eq 4 \) (doesn't match). So option A is correct.

Answer:

Table Completion:

• When \( x = 2 \), \( y = 6 \)
• When \( x = 3 \), \( y = 4 \)
• When \( x = 4 \), \( y = 2 \)

Rule:

A. Multiply \( x \) by 2. Subtract the product from 10 to get \( y \).