Question

Are y=7/3x+6 and y=-3/7x+4 lines parallel perpendicular or neither?I just need a brief explanation with the answer

Answer 1

Step 1: Theorem

Two lines are perpendicular if the product of their slope is equal to -1.

Two lines are parallel if their slope is equal.

Step 2:

$\begin{gathered} \text{Write the general equation of a line in slope-intercept form} \\ y\text{ = mx + c} \\ \text{m = slope} \end{gathered}$

Step 3:

Determine the slope from each equation

$\begin{gathered} y\text{ = }\frac{7}{3}\text{ x + 6} \\ m_1\text{ = }\frac{7}{3} \\ y\text{ = }\frac{-3}{7}x\text{ + 4} \\ m_2\text{ = }\frac{-3}{7} \end{gathered}$

Step 4: Determine if the two lines are parallel or perpendicular.

$\begin{gathered} m_1\text{ }\ne m_2\text{ hence the lines are not parallel} \\ m_1\text{ }\times m_2\text{ = }\frac{7}{3}\text{ }\times\text{ }\frac{-3}{7}\text{ = }\frac{-27}{27}\text{ = -1} \end{gathered}$

Final answer

Since the product of the two lines is equal to -1, hence, the two lines are perpendicular.

Perpendicular