line axis intersectioni don't get what to do to find intersection of a line and x and y axis.

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

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).

pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

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.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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).

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