General Form into Intercept Form

We will learn the transformation of general form into intercept form.

To reduce the general equation ax + by + c = 0 into intercept form (\(\frac{x}{a}\) + \(\frac{y}{b}\) = 1):

We have the general equation ax + by + c = 0.

If a ≠ 0, b ≠ 0, c ≠ 0 then from the given equation we get, 

ax + by = - c (Subtracting c from both sides)

⇒ \(\frac{ax}{-c}\) + \(\frac{by}{-c}\) = \(\frac{-c}{-c}\), (Dividing both sides by -c)

⇒ \(\frac{ax}{-c}\) + \(\frac{by}{-c}\) = 1

⇒ \(\frac{x}{-\frac{c}{a}}\) + \(\frac{y}{-\frac{c}{b}}\) = 1, which is the required intercept form (\(\frac{x}{a}\) + \(\frac{y}{b}\) = 1) of the general form of line ax + by + c = 0.

Thus, for the straight line ax + by + c = 0,

Intercept on x-axis = -(\(\frac{c}{a}\))  = - \(\frac{\textrm{Constant term}}{\textrm{Coefficient of x}}\)

Intercept on y-axis = -(\(\frac{c}{b}\))  = - \(\frac{\textrm{Constant term}}{\textrm{Coefficient of y}}\)


Note: From the above discussion we conclude that the intercepts made by a straight line with the co-ordinate axes can be determined by transforming its equation to intercept form. To determine the intercepts on the co-ordinate axes we can also use the following method:

To find the intercept on x-axis (i.e., x-intercept), put y = 0 in the given equation of the straight line line and find the value of x. Similarly To find the intercept on y-axis (i.e., y-intercept), put x = 0 in the given equation of the straight line and find the value of y.


Solved examples on transformation of general equation into intercept form:

1. Transform the equation of the straight line 3x + 2y - 18 = 0 to intercept form and find its x-intercept and y-intercept.

Solution:

The given equation of the straight line 3x + 2y - 18 = 0

First add 18 on both sides.

⇒ 3x + 2y =18

Now divide both sides by 18

⇒ \(\frac{3x}{18}\) + \(\frac{2y}{18}\) = \(\frac{18}{18}\)

⇒ \(\frac{x}{6}\) + \(\frac{y}{9}\)  = 1,

which is the required intercept form of the given straight line 3x + 2y - 18 = 0.

Therefore, x-intercept = 6 and y-intercept = 9.

 

2. Reduce the equation -5x + 4y = 8 into intercept form and find its intercepts.

Solution:

The given equation of the straight line -7x + 4y = -8.

First divide both sides by -8

⇒ \(\frac{-7x}{-8}\) + \(\frac{4y}{-8}\) = \(\frac{-8x}{-8}\)

⇒ \(\frac{7x}{8}\) + \(\frac{y}{-2}\) = 1

⇒ \(\frac{x}{\frac{8}{7}}\) + \(\frac{y}{-2}\) = 1,

which is the required intercept form of the given straight line -5x + 4y = 8.

Therefore, x-intercept = \(\frac{8}{7}\)  and y-intercept = -2.

 The Straight Line






11 and 12 Grade Math 

From General Form into 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 Word Problems on Fractions | Fraction Word Problems | Ans

    Jul 16, 24 02:20 AM

    In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

    Read More

  2. Word Problems on Fraction | Math Fraction Word Problems |Fraction Math

    Jul 16, 24 01:36 AM

    In word problems on fraction we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

    Read More

  3. Worksheet on Add and Subtract Fractions | Word Problems | Fractions

    Jul 16, 24 12:17 AM

    Worksheet on Add and Subtract Fractions
    Recall the topic carefully and practice the questions given in the math worksheet on add and subtract fractions. The question mainly covers addition with the help of a fraction number line, subtractio…

    Read More

  4. Comparison of Like Fractions | Comparing Fractions | Like Fractions

    Jul 15, 24 03:22 PM

    Comparison of Like Fractions
    Any two like fractions can be compared by comparing their numerators. The fraction with larger numerator is greater than the fraction with smaller numerator, for example \(\frac{7}{13}\) > \(\frac{2…

    Read More

  5. Worksheet on Reducing Fraction | Simplifying Fractions | Lowest Form

    Jul 15, 24 03:17 PM

    Worksheet on Reducing Fraction
    Practice the questions given in the math worksheet on reducing fraction to the lowest terms by using division. Fractional numbers are given in the questions to reduce to its lowest term.

    Read More