Question

(3.07A MC)

The graph shows two lines, A and B:

A graph is shown with x and y axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 6 with the ordered pair 5, 0. Another straight line labeled B joins the ordered pair 0, 2 with the ordered pair 6, 6.

Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?

(3, 4) is the solution to both lines A and B.
(3, 4) is the solution to line A but not to line B.
(0, 2) is the solution to both lines A and B.
(0, 2) is the solution to line A but not to line B.

Answer 1

• (3, 4) is the solution to both lines A and B.

Explanation:

Given

• Line A with points (2, 6) and (5, 0)
• Line B with points (0, 2) and (6, 6)

Lets get the equations for both lines

Line A

• y = mx + b
• m = (0 - 6)/( 5 - 2) = -2
• 6 = 2*(-2) + b ⇒ b = 6+ 4 = 10
• y = - 2x + 10

Line B

• m = (6 - 2)/( 6 - 0) = 4/6 = 2/3
• b = 2 as per point (0, 2)
• y = 2/3x + 2

We got two equations:

• y = -2x + 10
• y = 2/3x + 2

Solving the system:

• -2x + 10 = 2/3x + 2
• 8/3x = 8
• x = 3 ⇒ y = 4
• (3, 4)

Verifying answer options

• (3, 4) is the solution to both lines A and B. YES
• (3, 4) is the solution to line A but not to line B. NO
• (0, 2) is the solution to both lines A and B. NO
• (0, 2) is the solution to line A but not to line B. NO