Let the line be y = mx + b
The x-axis is given by the equation y= 0
To find the intersection between the line and the x-axis we find the points where y= y
==> mx + b = 0
Then, we solve for x.
Let the solution be x1.
Then, the intersection point between the line and the x-axis is (x1, 0).
Now we know that the equation for the y-axis is x = 0.
==> Then, we will substitute with x= 0 into the equation of the line.
==> y= b
Then the intersection point between the line and the y-axis is ( 0, b).
This depends on what you know about the line. If you have the equation for the line, it's pretty easy to find the intercepts.
You know that the x intercept, for example, is the point on the line where y = 0. So you take the equation and set y = 0 and solve for x. Then you will have the coordinates of the x intercept. Then you can do the same for the y intercept -- just set x = 0 and solve for y.
We know that when a line is intersecting x axis, the value of x is the solution of the equation.
We'll have the equation of the line y = ax + b (1).
Whne we want to find the solution of the equation of the line, we write:
ax + b = 0 (2)
x = -b/a
Comparing (1) and (2), we'll get y = 0.
So, the line is intercepting x axis in the point (-b/a , 0).
We'll conclude that if we want to find out the y intercepting point, we'll have to put x = 0.
y = ax + b
For x = 0 => y = a*0 + b
y = b
So, the line is intercepting y axis in the point (0 , b).