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 0, 6 with the ordered pair 6, 3. Another straight line labeled B joins the ordered pair 0, 0 with the ordered pair 6, 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

Solution :-

given that, A straight line labelled A joins the ordered pair 0, 6 with the ordered pair 6, 3.

so,

→ Slope of line A = (y2 - y1)/(x2 - x1) = (3 - 6)/(6 - 0) = (-3)/6 = (-1/2)

then, equation of line will be,

→ y - y1 = m(x - x1)

→ y - 6 = (-1/2)(x - 0)

→ 2y - 12 = (-x)

→ x + 2y = 12 ---------- Eqn.(1)

similarly, B joins the ordered pair 0, 0 with the ordered pair 6, 6.

→ Slope of line B = (y2 - y1)/(x2 - x1) = (6 - 0)/(6 - 0) = 6/6 = 1

then, equation of line will be,

→ y - y1 = m(x - x1)

→ y - 0 = 1(x - 0)

→ y = x ---------- Eqn.(2)

putting value of y in Eqn.(1),

→ x + 2x = 12

→ 3x = 12

→ x = 4 .

therefore, the solution to the equations of lines A and B is (4,4) .

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