Question

a. same-side interior angles
b. alternate exterior angles
c. alternate interior angles
d. corresponding angles

1. what is the relationship between $\angle3$ and $\angle6$

a. same-side interior angles
b. corresponding angles
c. alternate exterior angles
d. alternate interior angles
write an equation for the line that is parallel to the given line and passes through the given point.

1. $y = 2x + 10; (3, 9)$

a. $y = 2x + 3$
b. $y = \frac{1}{2}x + 3$
c. $y = 2x - 15$
d. $y = -\frac{1}{2}x - 3$

Explanation:

Step1: Identify ∠3 and ∠6 positions

∠3 and ∠6 lie between the two parallel lines \(m\) and \(n\), on opposite sides of the transversal.

Step2: Match to angle relationship

This fits the definition of alternate interior angles.

Step3: Recall parallel line slope rule

Parallel lines have equal slopes. Given line \(y=2x+10\), slope \(m=2\).

Step4: Use point-slope form

Point-slope formula: \(y - y_1 = m(x - x_1)\), substitute \((x_1,y_1)=(3,9)\), \(m=2\)
\(y - 9 = 2(x - 3)\)

Step5: Simplify to slope-intercept form

\(y - 9 = 2x - 6\)
\(y = 2x - 6 + 9\)
\(y = 2x + 3\)

Answer:

1. d. alternate interior angles
2. a. \(y = 2x + 3\)