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

Answer:

A. one  B. (3, 4)

Step-by-step 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 $m=\frac{6-0}{2-5}=\frac{6}{-3}=-2$

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 $m=\frac{6-2}{6-0}=\frac{2}{3}$

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

$y-2=\frac{2}{3}(x-0)\\y=\frac{2}{3}x+2$

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

$-2x+10=\frac{2}{3}x+2\\-6x+30=2x+6\\-8x=-24\\x=3$

Find y using either equation to get y = 4.