Question

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.

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

A. one B. (3, 4)

Explanation:

1. A good graph can answer both parts (see attached image).

2. Write equations for the two lines and find a simultaneous solution.

Line A: Slope from (2, 6) to (5, 0) is
`m=(6-0)/(2-5)=(6)/(-3)=-2`

Using point-slope form
`y-y_1=m(x-x_1)`

`y-6=-2(x-2)\\y-6=-2x+4\\y=-2x+10`

Line B: Slopt from (6, 6) to (0, 2) is
`m=(6-2)/(6-0)=(2)/(3)`

Using point-slope form, the equation for Line B is

`y-2=(2)/(3)(x-0)\\y=(2)/(3)x+2`

To find the simultaneous solution, set the y's equal.

`-2x+10=(2)/(3)x+2\\-6x+30=2x+6\\-8x=-24\\x=3`

Find y using either equation to get y = 4.