Question

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 6, 2. Another straight line labeled B joins the ordered pair 0, 3 with the ordered pair 4.5, 6. Part A: How many solutions does the pair of equations for lines A and B have? Explain your answer. (5 points) Part B: What is the solution to the equations of lines A and B? Explain your answer. (5 points)

Answer 1

there will be one solution because the lines intersect at exactly one set of points.

(0,6)(6,3)
slope(m) = (3-6) / (6-0) = -3/6 = -1/2

y = mx + b
6 = -1/2(0) + b
6 = b
y = -1/2x + 6

(0,0)(6,6)
slope(m) = (6-0) / (6-0) = 6/6 = 1

y = mx + b
6 = 1(6) + b
6 = 6 + b
6 - 6 = b
0 = b

y = x + 0

x = -1/2x + 6
1/2x + x = 6
1/2x + 2/2x = 6
3/2x = 6
x = 6/(3/2)
x = 6 * 2/3
x = 12/3 = 4

solution is : (4,4)