Question

complete the table. then, plot the pairs of values on the coordinate plane.

let x be the first row of values. let y be the second row of values. choose the correct graph below

a.

b.

c.

d.

Explanation:

Step1: Analyze the table

The first row (x) has values 2, 4, 6, 8, 10. The second row (y) starts with 8. Let's find the relationship between x and y. For x = 2, y = 8. Let's assume a linear relationship \( y = kx \). Then \( k=\frac{y}{x}=\frac{8}{2} = 4 \). So the equation is \( y = 4x \).

Step2: Check the graphs

• For graph A: When x = 2, y = 8 (since \( 4\times2 = 8 \)), x = 4, y = 16 (\( 4\times4 = 16 \)), x = 6, y = 24 (\( 4\times6 = 24 \)), x = 8, y = 32 (\( 4\times8 = 32 \)), x = 10, y = 40 (\( 4\times10 = 40 \)). The graph A seems to match these points (the points on graph A are at (2,8), (4,16), (6,24), etc. as per the grid).
• Graph B: The y - axis and x - axis scales are different. For x = 2, y should be 8, but in graph B, the y - axis at x = 2 is around 4, which does not match \( y = 4x \).
• Graph C: The point shown is not consistent with \( y = 4x \) (for x values 2,4,6,8,10, the y - values should be 8,16,24,32,40, not the point shown in C).
• Graph D: The line is not consistent with the linear relationship \( y = 4x \).

Answer:

A. The graph labeled A (with the y - axis up to 48 and x - axis up to 12, showing points consistent with \( y = 4x \))