X and Y intercept form calculator:

X and Y intercept form calculator finds the point of intersection of a line on the cartesian coordinates using the coefficients of the equation of the line. This calculator evaluates the x-intercept and y-intercept of the given equation.  This method of the equation of the line finds the values without using the slope of the line.

What is an intercept?

In mathematics, the intercept is a point where the line crosses the ordinate. The intercept has two types known as X and Y intercepts. The X intercept of a line indicates the point of intersection on the abscissa, whereas the y-intercept indicates the same on the y-axis.  

How can we calculate the X and Y intercepts of a line?

Try our X and Y intercept form calculator to calculate it. Or follow the following steps to calculate it manually.

• First of all, check whether the equation is linear or not.
• After checking the linearity re-arrange the equation in Ax + By + C = 0 form.
• For the x-intercept put y = 0 in the equation and calculate it using specific arithmetic operations.
• For the y-intercept, put x=0 and calculate it.

The following examples will help you to understand the procedure more clearly.

Example 1:

Calculate the X and Y intercepts of the equation 8x + 2y + 4 = 0

Solution:

The given equation is 8x + 2y+ 4 = 0

Step 1: Check the linearity:

The maximum power of the given equation is “1” so it is linear.

As the equation is already arranged so we’ll move toward the calculations.

For x-intercept:

8x + 2y+ 4 = 0

8x + 2y = - 4

Putt y = 0

 8x + 2(0) = - 4

8x + 0 = 4

8x = 4

x = 4/8

x = ½ or 0.50

For y-intercept:

8x + 2y+ 4 = 0

Put x = 0,

8 (0) + 2y = 4

0 + 2y = 4

2y = 4

Y = 4/2 or 2

The intercepts are (0.50, 2)

Example 2:

Calculate the X and Y intercepts of the equation if A = 4, B = 9 and C = 1

Solution:

The given points are A = 4, B = 9 and C = 1

The general formula for the equation of a line is:

Ax + By + C = 0

Put the points in the above formula we get:

4x + 9y + 1 = 0

For x-intercept:

4x + 9y = -1

Put y = 0

4x + 9(0) = -1

4x = -1

X = -1/4

For y-intercept:

4x + 9y = -1

Put x = 0

4 (0) + 9y = -1

0 + 9y = -1

9y = -1

Y = -1/9

The intercepts are (-1/4, -1/9)

References

1. Intercepts of Lines Review (X-intercepts and Y-intercepts)| Khan Academy.