Answer:
[tex]p:y = 3x-10[/tex]
Step-by-step explanation:
We are given the following in the question:
A(1, 1), B(2, 4), C(4, 2)
i) Slope of AB
[tex]A(1, 1), B(2, 4)\\\\m = \dfrac{y_2-y_1}{x_2-x_1}\\\\m = \dfrac{4-1}{2-1}=3[/tex]
Thus, slope of AB is 3.
ii) Point slope form
The point slope form of a line can be written as:
[tex]y - y_1 = m(x - x_1)[/tex]
The point intercept form of line can be written as:
[tex]y = mx + c[/tex]
The line is parallel to AB and contains point C(4, 2). Since line p is parallel to AB, line p will have the same slope as line AB
Putting values, we get,
[tex]y - 2 = 3(x-4)\\y = 3x-12+2\\y = 3x-10[/tex]
which is the required slope intercept equation of line p.
