Question

Part 1: Create an equation of a line in point-slope form. Be sure to identify all parts of the equation before writing the equation.

Part 2: Using the equation of the line you wrote in part 1, write an equation of a line that is perpendicular to this line.

Answer 1

Equation:

y-y1=m(x-x1)

y-2=4(x-1)

Part 2:

y=-1/4x +b

Explanation:

Answer 2

Answer with explanation:

Part--1:

We know that a equation in point-slope form is represented by:

`y-y_1=m(x-x_1)`

where m is the slope of the line and
`(x_,y_1)` is a point through which the line passes.

Consider a equation in a point-slope form as:

`y-5=2(x-1)`

This means that the slope of the line is: 5

and the line passes through the point (1,5).

Part--2:

Now as we know that if a line has a slope as m then the perpendicular line has a slope: -1/m

Since,

`m* \text{Slope\ of\ second\ line}=-1\\\\i.e.\\\\\text{Slope\ of\ second\ line}=(-1)/(m)`

Let this perpendicular line passes through (2,6)

Hence, the equation of a line in point slope form is given by:

`y-6=(-1)/(2)(x-2)`