![\"\"](\"https:\/\/asavana.com\/sites\/default\/files\/u53\/file3.PNG\")
<\/p>\nTo find the angle line using the y-axis, you'll need the\u00a0equation of a line in reference to the vertical line. When dealing with graphs, the x- and y-axis are\u00a0considered codependent. The x-axis is usually referred to as the independent variable, while the y-axis belongs to the dependent variable.<\/p>\n
Let\u2019s 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\u00a0unique name. How would this appear on a graph?<\/p>\n
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\u00a0that 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\u00a0the x-axis. Y is either high or low, depending on the name.<\/p>\n
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.<\/p>\n
<\/p>\n
The equation of a line is y = mx +c.<\/p>\n
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.<\/p>\n
<\/p>\n
![\"A](\"https:\/\/asavana.com\/sites\/default\/files\/u53\/file%202.PNG\")
<\/p>\n
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\u2019s from 0 to 90 degrees. An angle that falls between 91 to 180 degrees is in the second quadrant.<\/p>\n
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. \u00a0When dealing with negative lines, it goes clockwise instead, which means an angle of -70 degrees is in the second quadrant.<\/p>\n
Also keep in mind that in the equation y = mx + c, m = tan\u03b8 and tan \u03b8 = dy\/dx.\u00a0 \u03b8 = tan-1dy\/dx<\/p>\n
Now, the angle with the y-axis is given as:<\/p>\n
Quadrant \u2013 \u03b8 = Quadrant \u2013 tan-1dy\/dx<\/p>\n
Let\u2019s assume the equation for a line is given as 5x - 5y + 15 = 0. Find the Angle Line Using the Y-Axis<\/p>\n
The first step would be to simplify.<\/p>\n
5x - 5y + 15 = 0 can also be written as 5y = 5x + 15<\/p>\n
Dividing both sides by 5<\/p>\n
y = x + 3<\/p>\n
This means that m = 1 and c = 3.<\/p>\n
1 = tan \u03b8 and \u03b8 is the angle that we are looking for.<\/p>\n
\u03b8 \u00a0= tan-1(1)<\/p>\n
\u03b8 \u00a0= 450<\/p>\n
This means the angle is 450, and it is in the first quadrant.<\/p>\n
Let\u2019s assume the equation for a line is given as 9x - 18y + 36 = 0. Find the Angle Line Using the Y-Axis.<\/p>\n
The first step would be to simplify.<\/p>\n
9x - 18y + 36 = 0 can also be written as 18y = 9x + 36<\/p>\n
Dividing both sides by 18<\/p>\n
y = 1\/2x + 2<\/p>\n
This means that m = 1\/2 and c = 2.<\/p>\n
1\/2 = tan \u03b8 and \u03b8\u00a0 is the angle that we are looking for.<\/p>\n
\u03b8 \u00a0= tan-1(1\/2)<\/p>\n
\u03b8 \u00a0= 26.60<\/p>\n
This means the angle is 450, and it is in the first quadrant.<\/p>\n
Let\u2019s assume the equation for a line is given as 3y = 6 \u2013 15x. Find the Angle Line Using the Y-Axis.<\/p>\n
The first step would be to simplify.<\/p>\n
3y = 6 \u2013 15x can also be written as -15x + 6<\/p>\n
Dividing both sides by 3<\/p>\n
y = -5x + 2<\/p>\n
This means that m = -5 and c = 2.<\/p>\n
-5 = tanq and q is the angle that we are looking for.<\/p>\n
\u03b8 \u00a0= tan-1(-5)<\/p>\n
\u03b8 \u00a0= -78.690<\/p>\n
This means the angle is -78.690, and it is in the second quadrant.<\/p>\n
180 \u2013 78.690 = 101.310.<\/p>\n
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.<\/p>\n