Question

1. determine if the functions are parallel, perpendicular or neither (click for video #8)

( y = \frac { 2 } { 3 } x + 7 ) neither
( y = - \frac { 2 } { 3 } x + 1 )

1. given ( l parallel m ), tell whether the given angles are vertical, linear pairs, alternate interior angles, alternate exterior angles, corresponding angles or consecutive interior angles (click for video #9)

( angle 4, angle 5 )
( angle 3, angle 6 )
( angle 4, angle 8 )
( angle 1, angle 3 )

Explanation:

8. Step - by - Step Format

Step1: Recall the slope - intercept form \(y = mx + b\)

For the line \(y=\frac{2}{3}x + 7\), the slope \(m_1=\frac{2}{3}\). For the line \(y =-\frac{2}{3}x+1\), the slope \(m_2=-\frac{2}{3}\).

Step2: Check the condition for parallel lines

Two lines are parallel if \(m_1=m_2\). Since \(\frac{2}{3}
eq-\frac{2}{3}\), the lines are not parallel.

Step3: Check the condition for perpendicular lines

Two lines are perpendicular if \(m_1\times m_2=- 1\). Calculate \(m_1\times m_2=\frac{2}{3}\times(-\frac{2}{3})=-\frac{4}{9}
eq - 1\)

• For \(\angle4\) and \(\angle5\):
• Alternate interior angles are non - adjacent interior angles that lie on opposite sides of the transversal. When \(l\parallel m\), \(\angle4\) and \(\angle5\) are non - adjacent, lie between \(l\) and \(m\), and on opposite sides of the transversal \(n\).
• For \(\angle3\) and \(\angle6\):
• Consecutive interior angles (also known as same - side interior angles) are interior angles that lie on the same side of the transversal. \(\angle3\) and \(\angle6\) are between \(l\) and \(m\) and on the same side of the transversal \(n\).
• For \(\angle4\) and \(\angle8\):
• Corresponding angles are in the same relative position with respect to the parallel lines and the transversal. \(\angle4\) and \(\angle8\) are in the same "corner" position.
• For \(\angle1\) and \(\angle3\):
• Vertical angles are opposite angles formed by the intersection of two lines. \(\angle1\) and \(\angle3\) are opposite angles formed by the intersection of lines \(l\) and \(n\).

Answer:

The two lines are neither parallel nor perpendicular.

9. Answer - Explanation Format