# Finding The Angle Line Using the Y-Axis

By Kathleen Cantor, 10 Sep 2020

To find the angle line using the y-axis, you'll need the equation of a line in reference to the vertical line. When dealing with graphs, the x- and y-axis are considered codependent. The x-axis is usually referred to as the independent variable, while the y-axis belongs to the dependent variable.

## Dependent Variables

Let’s say you are conducting a theoretical study to determine how the name of a child affects his or her chances of success as an individual. Let's say that children with common names like Michael and Sarah have higher chances of doing well in life over those with a unique name. How would this appear on a graph?

The names included in the study are written on the x-axis of the graph. The rate of success is represented on the y-axis. This indicates that the names are the independent variables, and the success rate is the dependent variable. The values on the y-axis are dependent on the variable of the x-axis. Y is either high or low, depending on the name.

The origin is the point at which y and x-axis cross where their coordinates are (0, 0). For the x-axis and y-axis with only positive values, the origin is at the lower-left corner.

## The Equation of a Line

The equation of a line is y = mx +c.

In this equation, m refers to the slope of a line with reference to the x-axis, and c is the intercept on the y-axis. Essentially, the y-intercept is a point in which a line crosses the y-axis, and the x-intercept is the point at which a line crosses the x-axis. Simply put, a line intercepts on the y-axis when its coordinates are at zero. The same goes for the x-axis intercept.

## Determining the Quadrant to Use

A circle is 360 degrees and is divided into four equal angles or quadrants. Each quadrant is 90 degrees, and it goes anti-clockwise. An angle falls in the first quadrant when it’s from 0 to 90 degrees. An angle that falls between 91 to 180 degrees is in the second quadrant.

An angle from 181 to 270 degrees is in the first quadrant. The fourth quadrant contains angles from 271 to 360 degrees, which is a circle.  When dealing with negative lines, it goes clockwise instead, which means an angle of -70 degrees is in the second quadrant.

Also keep in mind that in the equation y = mx + c, m = tanθ and tan θ = dy/dx.  θ = tan-1dy/dx

Now, the angle with the y-axis is given as:

### Example 1

Let’s assume the equation for a line is given as 5x - 5y + 15 = 0. Find the Angle Line Using the Y-Axis

The first step would be to simplify.

5x - 5y + 15 = 0 can also be written as 5y = 5x + 15

Dividing both sides by 5

y = x + 3

This means that m = 1 and c = 3.

1 = tan θ and θ is the angle that we are looking for.

θ  = tan-1(1)

θ  = 450

This means the angle is 450, and it is in the first quadrant.

1. – 45 = 450.

### Example 2

Let’s assume the equation for a line is given as 9x - 18y + 36 = 0. Find the Angle Line Using the Y-Axis.

The first step would be to simplify.

9x - 18y + 36 = 0 can also be written as 18y = 9x + 36

Dividing both sides by 18

y = 1/2x + 2

This means that m = 1/2 and c = 2.

1/2 = tan θ and θ  is the angle that we are looking for.

θ  = tan-1(1/2)

θ  = 26.60

This means the angle is 450, and it is in the first quadrant.

1. – 26.6 = 63.40.

### Example 1

Let’s assume the equation for a line is given as 3y = 6 – 15x. Find the Angle Line Using the Y-Axis.

The first step would be to simplify.

3y = 6 – 15x can also be written as -15x + 6

Dividing both sides by 3

y = -5x + 2

This means that m = -5 and c = 2.

-5 = tanq and q is the angle that we are looking for.

θ  = tan-1(-5)

θ  = -78.690

This means the angle is -78.690, and it is in the second quadrant.

180 – 78.690 = 101.310.

For easier comprehension, familiarize yourself with a circle, and it's quadrants before trying to solve the equation of a line. If you do not know what quadrant a certain angle falls, you will get your angle wrong even if you did everything else right.

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