What is an equation of the line that passes through the point (1,3) and is
perpendicular to the line x + 3y = 9?

y = 2x + 0

y = mx + C - equation of the line

Step-by-step explanation:

First, find the slope

x + 3y = 9

Using the equation of line

y = mx + C

3y = 9 - x

3y = -x + 9

Divide both sides by 3

3y / 3 = ( -x + 9) / 3

y = ( -x + 9) / 3

We can separate it

y = -x/3 + 9/3

y = -x/3 + 3

m = -1/3

Slope = -1/3

Since weve gotten our slope

Let's use the equation of point slope form

y - y_1 = m(x - x_1)

We are provided with a point

( 1, 3)

x_1 = 1

y_1 = 3

If two lines are perpendicular, their slope will be negative reciprocal

m = -1/3

Perpendicular = +3/1

insert the values

y - 3 = 3(x - 1)

y - 3 = 3x - 3

y = 3x - 3 + 3

-3 cancels +3

y = 3x + 0

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.