Calculating the linear equation of the variables x and y is a crucial topic in the study of mathematics. We must comprehend the structure of the graph in order to determine the intercepts of the x and y axes. The x and y-axis intercepts are then determined. Understanding how to locate x and y intercepts is crucial. So let’s begin discussing x- and y-axis intercepts. Then we will move on to how to find x and y intercepts.
To find the x and y intercepts, first of all, we need the linear equation in which x and y functions are present. Then we solve it to get the solution. To solve the equation for x-intercept, we have to put y=0 and for y-intercept, we have to put x=0. It is very important for mathematics students that they understand all the terms and steps that how to find x and y intercepts.
To find x and y intercepts, you have to understand the graph and its axis. Before moving on to how to find x and y intercepts let’s learn about graphs.
What is a graph?
The graph is that in which we design the diagram, like lines, points, line segments, curves, areas, etc. The graph is that thing through which we can represent the data with every focus point and understands all vertices and points on the graph. To show everything related to the data we need to plot the graph.
It is the collection of points of vertices and edges that join pairs of vertices.
This is a two-dimensional graph. A two-dimensional graph is a graph in which we have only two points, x, and y. In this, we draw the graph only in the x and y plan. You can see in the graph that there are only two plans x and y.
Graphs are also three-dimensional, whereas in this graph the z-axis is also involved. In a three-dimensional graph, the z-axis is also involved. That point that intersects the z-axis, that point refers to the z-intercept.
What are the x and y axis and their intercepts?
To understand the x and y intercepts, first of all, you need to understand what is the x-axis and y-axis. Then you have the solution to your query: how to find x and y intercepts.
What is the x and y axis?
- The X axis is the horizontal line which is a plot on the graph.
- The Y axis is the vertical line that is a plot on the graph.
What are the x and y intercepts?
When we draw any line or curve on the graph, then we have the points which intersect the x-axis. That intersection point on the x-axis refers to the x-intercepts.
The X-intercept is that point that crosses the x-axis.
When we plot any line or curve on the graph, then we have the intersection points on the y-axis. That intersection point on the y-axis refers to the y-intercepts.
The Y-intercept is that point that crosses the y-axis.
So it is very important for you that you know how to find x and y intercepts.
How to find x and y intercepts?
To find the x-intercept, we have to put y=0 in the equation.
Because when we put y=0, then we have the value of the x variable.
For example:- The linear equation is x-y-10=0.
Put y=o, and then we have, x=10
The point is (10,0).
To find y-intercepts, we have to put x=0 in the equation.
Because when we put x=0, then we have the value of the y variable.
Put x=0 in the above equation, and then we have, y=-10
The point is (0,-10).
From that solution, x=10 and y=-10 are the x and y intercepts.
X and y intercepts on the graph show that.
After understanding the steps and process, we can get the answer to that query about how to find x and y intercepts.
Here are some more examples of x and y intercepts.
Example 1
- 2x+y=22
- Put y=0, and then we have 2x=22
- x=11
- This is the x-intercept.
- Put x=0, and then we have y=22
- This is the y-intercept.
- The points are (11,0) and (0,22).
- From this example, x=10 and y=22 are the intercepts.
Example 2
- 5x+3y=30
- Put y=0, and then we have 5x=30
- x=6
- This is the x-intercept.
- Put x=0, and then we have 3y=30
- y=10
- This is the y-intercept.
- The points are (6,0) and (0,10).
- From that example, x=6 and y=10 are the intercepts.
Example 3
- 2x+5y=20
- Put y=0, and then we have 2x = 20.
- x=10
- This is the x-intercept.
- Put x=0, and then we have 5y = 20.
- y=4
- This is the y-intercept.
- The points are (10,0) and (0,4).
- From that example, x=10 and y=4 are the intercepts.
Example 4
- 3x+6y=12
- Put y=0, and then we have 3x=12
- x=4
- This is the x-intercept.
- Put x=0, and then we have 6y=12
- y=2
- This is the y-intercept.
- The points are (4,0) and (0,2).
- From that example, x=4 and y=2 are the intercepts.
- 4x+6y=24
- Put y=0, and then we have 4x=24
- x=6
- This is the x-intercept.
- Put x=0, and then we have 6y=24
- y=4
- This is the y-intercept.
- The points are (6,0) and (0,4).
- From that example, x=6 and y=4 are the intercepts.
Example 5
- 9x-6y=54
- Put y=0, and then we have 9x=54
- x=6
- This is the x-intercept.
- Put x=0, and then we have -6y=54
- y=-9
- This is the y-intercept.
- The points are (6,0) and (0,-9).
- From this example, x=6 and y=-9 are the intercepts.
Example 6
- x+2y=40
- Put y=0, and then we have x=40
- This is the x-intercept.
- Put x=0, and then we have 2y=40
- y=20
- This is the y-intercept.
- The points are (40,0) and (0,20).
- From this example, x=40 and y=20 are the intercepts.
Example 7
- 8x+6y=48
- Put y=0, and then we have 8x=48
- x=6
- This is the x-intercept.
- Put x=0, and then we have 6y=48
- y=8
- This is the y-intercept.
- The points are (6,0) and (0,8).
- From this example, x=6 and y=8 are the intercepts.
Example 8
- 7x-y=35
- Put y=0, and then we have 7x=35
- x=5
- This is the x-intercept.
- Put x=0, and then we have -y=35
- y=-35
- This is the y-intercept.
- The points are (5,0) and (0,-35).
- From this example, x=5 and y=-35 are intercepting.
Example 9
- 8x-5y+40=0
- Put y=0, and then we have 8x+40=0
- 8x=-40
- x=-5
- This is the x-intercept.
- Put x=0 then we have -5y+40=0
- -5y=-40
- y=8
- This is the y-intercept.
- The points are (-5,0) and (0,8).
- From that example, x=-5 and y=8 are the intercepts.
These are some examples that help you to understand the x and y-intercept, and you get the answer to your question of how to find x and y intercepts.
Conclusion
In this article, we discuss the x and y intercepts. In this article, we explained all the points and steps on how to find x and y intercepts. I hope that the article helps you to understand those terms and that you will succeed in understanding that topic.
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