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 stra

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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