X and Y Intercept Formula

X and Y Intercept Formula as the name suggests, is the formula to calculate the intercept of a given straight line. An intercept is defined as the point at which the line or curve intersects the graph’s axis. The intercept of a line is the point at which it intersects the x-axis or the y-axis.

When an equation isn’t in the form y = mx + b, we determine the intercepts by substituting 0 as necessary and solving for the corresponding variable.

• To find the y-intercept, we set x = 0 and solve for y. This yields the point (0,y).
• To find the x-intercept, we set y = 0 and solve for x. This gives us the point (x,0).

An intercept is defined as the point where the line or curve crosses the axis. If the point is on the x-axis then it is called the x-intercept and if the point is on the y-axis, then it is called the y-intercept.

We generally represent the x-intercept by a and the y-intercept by b. The equation of the line making a and b intercept on the x and y axis respectively is,

x/a + y/b = 1

The x-intercept of a line is the point at which the line intersects the x-axis. So, to find the x-intercept put y = 0 in the equation of a line. 

The formula of x-intercept for slope-intercept equation y = mx + c is given by,

x-intercept = -c/m

Thus, (-c/m, 0) is the coordinate of x-intercept.

Where,

• (0, c) is the y-intercept,
• m is the slope of the given line.

Consider a line given in the slope intercept form y = mx + c, where the line has a intercept (c, 0) and has a slope m.

Put y = 0 in the equation to get the x-intercept.

⇒ 0 = mx + c

Solve the equation for x.

⇒  mx = -c

⇒ x = -c/m

This derives the formula for x-intercept.

Check: Slope Intercept Form of line

The y-intercept of a line is the point at which the line intersects the y-axis. So, to find the y-intercept, put x = 0 in the equation of a line. 

The formula of y-intercept for slope-intercept equation y = mx + c is given by,

y-intercept = c

Thus, (0, c) is the coordinate of y-intercept.

Consider a line given in the slope-intercept form y = mx + c, where the line passes through the point (0, c) and has a slope m.

Put x = 0 in the equation to get the y-intercept.

⇒  y = m (0) + c

⇒  y = 0 + c

⇒  y = c

This derives the formula for y-intercept.

To find the x-intercept we put y = 0 in the given function and then solve for x. The resultant value of x is the x-intercept of the given function.

Example: Find the x-intercept of the linear equation 2x + 3y = 7.

Solution:

For the x-intercept of the linear equation 2x + 3y = 7

Put y = 0,

2x + 3×0 = 7

⇒ x = 7/2

Thus, the x-intercept of 2x + 3y = 7 is 7/2.

To find the y-intercept we put x = 0 in the given function and then solve for y. The resultant value of y is the y-intercept of the given function.

Example: Find the y-intercept of the linear equation 3x + 4y = 12.

Solution:

For the y-intercept of the linear equation  3x + 4y = 12

Put x = 0,

3×0 + 4y = 12

⇒ y = 12/4

⇒ y = 3

Thus, the y-intercept of 3x + 4y = 12 is 3.

Intercept Form of a Straight Line, mathematically given by 

x/a + y/b = 1

Where, 

• a is the x-intercept of the straight line
• b is the y-intercept of the straight line

We know that the intercept is the points on the axes that are cut by a straight line. The point on the x-axis is called the x-intercept, and the point on the y-axis is called the y-intercept. The image added below shows the line, with x and y intercepts.

The point-slope form of a line is given as follows:

y – y₁ = m(x – x₁)

where:

• (x₁, y₁) is a point on the line
• m is the slope of the line.

To find, the x and y-intercepts of the given line,

Here, rearranging the equation, we get

y = mx – mx₁ + y₁

⇒ y = mx + (-mx₁ + y₁)

Comparing it with y = mx + c, we get

c = -mx₁ + y₁, which is the y-intercept of the given line.

and x-intercept is -c/m = (mx₁ – y₁)/m = x₁ – y₁/m 

Thus, x and y-intercept of the given y – y₁ = m(x – x₁) are x₁ – y₁/m and  -mx₁ + y₁ respectively.

There are various use cases of X And Y Intercepts, some of which are as follows:

• We use the concept of intercepts in curve tracing, for example, we have an unknown curve, so intercepts are one of the first parameters in the analysis of the curve.
• Both intercepts in whichever quadrant forms a triangle, whose area can calculate by 1/2 times the product of intercepts.
• By plotting both intercepts on the coordinated axes, we can plot the graph of the linear equation.

Articles related to X and Y Intercept Formula:

• Equation of a Straight Line
• Point Slope Form
• Linear Equations

Problem 1: Calculate the x-intercept of the equation x + 3y = 8.

Solution:

We have the equation as, x + 3y = 8.

Put y = 0 to find the x-intercept and then solve the equation for x.

⇒  x + 3 (0) = 8

⇒  x = 8

So, the x-intercept for the equation is (8, 0).

Problem 2: Calculate the x-intercept of equation 4x + 7y = 10.

Solution:

We have the equation as, 4x + 7y = 10.

Put y = 0 to find the x-intercept and then solve the equation for x.

⇒  4x + 7 (0) = 10

⇒  4x = 10

⇒ x = 10/4

⇒  x = 5/2

So, the x-intercept for the equation is (5/2, 0).

Problem 3: Calculate the y-intercept of equation 4x + 3y = 24.

Solution:

We have the equation as, 4x + 3y = 24.

Put x = 0 to find the y-intercept and then solve the equation for y.

⇒ 4(0) + 3y = 24

⇒  3y = 24

⇒  y = 24/3

⇒  y = 8

So, the y-intercept for the equation is (0, 8).

Problem 4: Calculate the y-intercept of equation 8x + 5y = 25.

Solution:

We have the equation as, 8x + 5y = 25.

Put x = 0 to find the y-intercept and then solve the equation for y.

⇒  8(0) + 5y = 25

⇒ 5y = 25

⇒  y = 25/5

⇒  y = 5

So, the y-intercept for the equation is (0, 5).

Problem 5: Calculate the x- and y-intercept of equation 4x² + 9y² = 25.

Solution:

We have the equation as, 4x² + 9y² = 25.

Put y = 0 to find the x-intercept and then solve the equation for x.

⇒  4x² + 9 (0)² = 25

⇒  4x² = 25

⇒  x² = 25/4

⇒  x = ±5/2

So, the x-intercept for the equation is (±5/2, 0).

Put x = 0 to find the y-intercept and then solve the equation for y.

⇒  4 (0)² + 9y² = 25

⇒  9y² = 25

⇒  y² = 25/9

⇒ y = ±5/3

So, the y-intercept for the equation is (0, ±5/3).

1. Find the x and y intercepts of the equation 3x – 2y = 6

2. Determine the x and y intercepts of the line represented by the equation 2y + 4x = 8

3. Find the x and y intercepts of the equation y = 2x – 3

4. Determine the x and y intercepts of the line represented by the equation 4x + 3y = 12

5. Find the x and y intercepts of the equation 5y – 2x = 10

What is the X-Intercept Formula?

For straight line y = mx + c, formula for x-intercept is given as follows:

x-intercept = -c/m

Thus,  (-c/m, 0) is the coordinate of x-intercept.

Where,

• (0, c) is the y-intercept,
• m is the slope of the given line.

What is the Y-Intercept Formula?

For straight line y = mx + c, formula for y-intercept is given as follows:

y-intercept = c

Thus, (0, c) is the coordinate of y-intercept.

How do you find the X-Intercept of a Linear Equation?

As x-intercept is the point where the line intersects the x-axis. Thus, we can find the coordinate of the x-intercept by putting (x,0) in the given linear equation and then finding the value of x. Thus, (x, 0) is the coordinate of the x-intercept.

How do you find the Y-Intercept of a Linear Equation?

As y-intercept is the point where the line intersects the y-axis. Thus, we can find the coordinate of the y-intercept by putting (0, y) in the given linear equation and then finding the value of y. Thus, (0, y) is the coordinate of the y-intercept.

What is the relationship between X-Intercept and Y-Intercept?

The relationship between the x and y-intercept is the slope of the line.