Question

ANOTHER BIG QUESTION, 100 POINTS

Answer 1

Slope of AB

• m=4-1/2-1=3/1=3

Point C(4,2)

Parallel lines have equal slope

• slope of p=3

Equation in point slope form

• y-2=3(x-4)
• y-2=3x-12
• y=3x-10

Answer 2

Answer:

Slope of AB = 3

line p:  y = 3x - 10

see attached for graph

Step-by-step explanation:

Given vertices:

• A = (1, 1)
• B = (2, 4)
• C = (4, 2)

Slope of AB

$\textsf{let}\:(x_1,y_1)=(1,1)$

$\textsf{let}\:(x_2,y_2)=(2,4)$

$\implies \textsf{slope of AB}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{4-1}{2-1}=3$

Equation of line p

Use point C (4, 2) and the slope of AB in the point-slope form of a linear equation, then simplify to slope-intercept form:

$\begin{aligned}y-y_1 &=m(x-x_1)\\\implies y-2 &=3(x-4)\\y &=3x-10\\\end{aligned}$