Loading [MathJax]/jax/output/HTML-CSS/jax.js

Subscribe to our YouTube channel for the latest videos, updates, and tips.


Straight Line in Intercept Form

We will learn how to find the equation of a straight line in intercept form.

The equation of a line which cuts off intercepts a and b respectively from the x and y axes is xa + yb = 1.

Let the straight line AB intersects the x-axis at A and the y-axis at B where OA = a and OB = b.

Now we have to find the equation of the straight line AB.

Let P(x, y) be any point on the line AB. Draw PQ perpendicular on OX and PR perpendicular on OX. Then, join the points O and P. Now, PQ = y, OQ = x.

Clearly, we see that

Area of the ∆OAB = Area of the ∆OPA + Area of the ∆OPB

⇒ ½ OA ∙ OB = ½ ∙ OA ∙ PQ + ½ ∙ OB ∙ PR

⇒ ½ a ∙ b = ½ ∙ a ∙ y + ½ ∙ b ∙ x

⇒ ab = ay + bx

abab = ay+bxab, dividing both sides by ab

⇒ 1 = ayab + bxab

⇒ 1 = yb + xa

xa + yb = 1, which is the equation of the line in the intercept form.

The equation xa + yb = 1 is the satisfied by the co-ordinates of any point P lying on the line AB.

Therefore, xa + yb = 1 represent the equation of the straight line AB.


Solved examples to find the equation of a straight line in intercept form:

1. Find the equation of the line which cuts off an intercept 3 on the positive direction of x-axis and an intercept 5 on the negative direction of y-axis.

Solution: 

The equation of a line which cuts off intercepts a and b respectively from the x and y axes is xa + yb = 1.

Here, a = 3 and b = -5

Therefore, the equation of the straight line is xa + yb = 1 ⇒ x3 + y5 = 1 ⇒ x3 - y5 = 1 ⇒ 5x – 3y = 15 ⇒ 5x – 3y – 15 = 0.

 

2. Find the intercepts of the straight line 4x + 3y = 24 on the co-ordinate axes.

Solution:

Given equation 4x + 3y = 24.

Now convert the given equation into intercept form.

4x + 3y = 24

4x+3y24 = 2424, Dividing both sides by 24

4x24 + 3y24 = 1

x6 + y8 = 1, which is the intercept form.

Therefore, x-intercept = 6 and y-intercept = 8.

Note: (i) The straight line xa + yb = 1 intersects the x-axis at A(a, 0) and the y-axis at B(0, b).

(ii) In xa + yb = 1, a is x-intercept and b is y- intercept.

These intercept a and b may be positive as well as negative.

(iii) If the straight line AB passing through the origin then, a = 0 and b = 0. If we put a = 0 and b = 0 in the intercept form, then x0 + y0 = 1, which is undefined. For this reason the equation of a straight line passing through the origin cannot be expressed in the intercept form.

(iv) A line parallel to the x-axis does not intercept the x-axis at any finite distance and hence, we cannot get any finite x- intercept (i.e., a) of such a line. For this reason, a line parallel to x-axis cannot be expressed in the intercept from. In like manner, we cannot get any finite y- intercept (i.e., b) of a line parallel to y-axis and hence, such a line cannot be expressed in the intercept form.

 The Straight Line







11 and 12 Grade Math

From Straight Line in Intercept Form to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Average | Word Problem on Average | Questions on Average

    May 19, 25 02:53 PM

    Worksheet on Average
    In worksheet on average we will solve different types of questions on the concept of average, calculating the average of the given quantities and application of average in different problems.

    Read More

  2. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More