Question

question 11: standard g.gpe.5
use point slope form to solve for the equation of a line that is parallel to y=2x+2 and that passes through the point (1,1).
a. y - 1 = 2(x - 1)
b. y - 3 = 2(x - 2)
c. y - 1 = 1(x - 2)
d. y - 1 = 2
question 12: standard g.gpe.5
use point slope form to solve for the equation of a line that is perpendicular to y = 1/4 x + 3 and passes through the point (3,2).
a. y - 3 = -4(x - 3)
b. y - 1 = 1/4(x - 2)
c. y - 6 = 1/4(x - 2)
d. y - 2 = -4(x - 3)

Explanation:

Question 11

Step1: Recall parallel lines have equal slopes.

The given line \( y = 2x + 2 \) has a slope \( m = 2 \). So the parallel line also has \( m = 2 \).

Step2: Recall point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(1,1) \) and \( m = 2 \).

Substitute \( x_1 = 1 \), \( y_1 = 1 \), and \( m = 2 \) into the point - slope formula: \( y-1 = 2(x - 1) \).

Step1: Recall perpendicular lines have slopes that are negative reciprocals.

The given line \( y=\frac{1}{4}x + 3 \) has a slope \( m_1=\frac{1}{4} \). The slope of a line perpendicular to it, \( m_2=-\frac{1}{m_1}=- 4 \).

Step2: Recall point - slope form \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(3,2) \) and \( m=-4 \).

Substitute \( x_1 = 3 \), \( y_1 = 2 \), and \( m=-4 \) into the point - slope formula: \( y - 2=-4(x - 3) \).

Answer:

a. \( y - 1=2(x - 1) \)

Question 12