Question

Choose the correct way to end the sentence.The lines 5x + 2y = 14 and y = –5x + 9 are_________.OptionsA. ParallelB. PerpendicularC. neither

Answer 1

Step 1:

Concept

Two lines are parallel if their slopes are equal.

Two lines are perpendicular if product of their slopes = -1

Step 2:

Find the slope of each line by writing each equation in the form of y = mx + c.

m = slope and c = intercept on y-axis

`\begin{gathered} \text{5x + 2y = 14} \\ 2y\text{ = -5x + 14} \\ y\text{ = }(-5)/(2)x\text{ + 7} \\ \text{Therefore, slope m}_1\text{ = }(-5)/(2) \\ \\ \text{Next,} \\ y\text{ = -5x + 9} \\ \text{slope m}_2\text{ = -5} \end{gathered}`

Final answer

`\begin{gathered} m_1\text{ }\\e m_2\text{ ( The two lines are not parallel)} \\ m_1m_2\text{ }\\e\text{ -1 ( The two lines are not perpendicular)} \\ \text{Hence, neither is the final answer} \end{gathered}`

Option C neither