Exercise 4 Page 187

There were two parts to Exploration $1,$ let's look at these individually and then compare our results.

Part A

We were given three equations and asked to write each of them in slope-intercept form: We were then asked to graph them and decide which ones appear to be parallel. Let's graph them all on the same coordinate plane. We can see that the parallel lines are: the ones represented by the red and blue lines.

Part B

Once again, we were given three equations and asked to write each of them in slope-intercept form: We can, again, graph the equations and decide which ones appear to be parallel. Let's graph them all on the same coordinate plane. We can see that the parallel lines are: the ones represented by the blue and green lines.

Conclusion

In A, the parallel lines were: In B, the parallel lines were: What do these pairs have in common? They have the same slope! It may not be totally obvious at first but remember that $\text{-}\frac{5}{2}=\text{-}2.5$ when you write it as a decimal. Two different lines with the same slope will always be parallel!