Intercepts From of Line

Intercept From of Line is,

x/a + y/b = 1

Where,

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

Finding Intercept Form Slope-Intercept Form of Line

The slope-Intercept Form of a straight line is,

y = mx + c

Where, 

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

For, this form of the line 

• x-intercept is given by  (-c/m, 0)
• y-intercept is given by (0, c)

Finding Intercept Form Point-Slope Form of Lines

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 

• x-Intercept is given by  x₁ – y₁/m
• y-Intercept is given by  -mx₁ + y₁

Finding Intercept Form Two Point Form of Line

If in the Point-slope Form of a line, we substitute the formula for slope, m = (y₂ – y₁)/(x₂ – x₁) we get the two-point Form of a Line, i.e.,

y – y₁ = (y₂ – y₁)/(x₂ – x₁)(x – x₁)

where,

• (x₁, y₁) and (x₂, y₂) are the two points from which line passes through.

Thus, x and y-intercept of the given y – y₁ = (y₂ – y₁)/(x₂ – x₁)(x – x₁) are 

• y-Intercept is given by x₁ – y₁(x₂ – x₁)/(y₂ – y₁)
• y-Intercept is given by -x₁(y₂ – y₁)/(x₂ – x₁) + y₁

X and Y-intercepts are the points on the coordinate axis where the graph of any given linear equation intersects. Intercepts are key concepts in the understanding of straight lines, which can reveal valuable information about the linear relationship of both variables.

In this article, we will explore the definition of intercepts including both x and y intercepts, intercepts in graphs, and intercept formulas for various forms of line. By the end of this article, you’ll have a solid understanding of X-intercepts and Y-intercepts and how to use them in real-world applications.