"Intercept form equation of a line" is one of the ways to express equation of a line.

Here, we will form equation of a straight line using x- intercept and y - intercept.

**Intercept form equation of a line**

Here,

**x- intercept = a**

**y- intercept = b**

**Problem 1 :**

If the x-intercept and y-intercept of a straight line are 2/3 and 3/4 respectively, find the general equation of the straight line.

**Solution :**

Given : x- intercept "a" = 2/3 and y-intercept "b" = 3/4

So, the equation of the straight line in intercept form is

x/a + y/b = 1

Plugging a = 2/3 and b = 3/4, we get

x / (2/3) + y / (3/4) = 1

3x / 2 + 4y / 3 = 1

(9x + 8y) / 6 = 1

9x + 8y = 6 -------> 9x + 8y - 6 = 0

**Hence the general equation of straight line is 9x + 8y - 6 = 0**

**Problem 2 :**

Find the equations of the straight lines each passing through the point (6, -2) and whose sum of the intercepts is 5.

**Solution :**

Let "a" and "b" be the x-intercept and y-intercept of the required straight line respectively.

**Given :** Sum of the intercepts = 5

So, we have a + b = 5 --------> b = 5 - a

Now, equation of the straight line in intercept form is

x/a + y/b = 1

Plugging b = 5 - a, we get

x / a + y / (5-a) = 1

[(5-a)x + ay ] / a(5-a) = 1

(5-a)x + ay = a(5-a) ----------(1)

**Since the straight line (1) is passing through (6, -2),**

we can plug x = 6 and y = -2 in (1)

(1) --------> (5 - a)6 - 2a = a(5 - a)

30 - 6a - 2a = 5a - a² ---------> a² - 13a + 30 = 0

a² - 13a + 30 = 0 -----------> (a - 10)(a - 3) = 0

a = 10 and a = 3

**When a = 10, **(1)------->(5 - 10)x + 10y = 10(5 - 10)

- 5x + 10y = - 50 -------> 5x - 10y - 50 = 0

5x - 10y - 50 = 0 -------> **x - 2y - 10 = 0**

**When a = 3,** (1)------->(5 - 3)x + 3y = 3(5 - 3)

2x + 3y = 6 --------> **2x + 3y - 6 = 0**

**Hence, x - 2y - 10 = 0 and 2x + 3y - 6 = 0 are the general equations of the required straight lines**

**Problem 3 :**

Find the x - intercept and y - intercept of the straight line whose equation is 5x + 3y - 15 = 0.

**Solution :**

To find the x - intercept and y - intercept of the line 5x + 3y -15 = 0, first we have to write the given equation in intercept form.

So, let us write the given equation in intercept form.

5x + 3y - 15 = 0

5x + 3y = 15

Divide by 15 on both sides,

(5x/15) + (3y/15) = 15/15

x/3 + y/5 = 1

The above equation is in intercept form.

**Hence, x- intercept is 3 and y - intercept is 5.**

Apart from intercept form equation of a straight line, we have some other different forms of equation of a straight line.

They are

(i) Slope intercept form

(ii) Point slope form

(iii) Two points form.

Let us look at the above different forms of equation of a straight line in detail.

Here,

**Slope of the line = m **

**y-intercept = b **

Here,

**Slope of the line = m **

**Point = (x₁ , y₁)**

Here, the two points are

**(x₁ , y₁) and (x₂ , y₂)**

Apart from the above forms of equation of straight line, there are some other ways to get equation of a straight line.

1. If a straight line is passing through a point (0,k) on y-axis and parallel to x-axis, then the equation of the straight line is y = k

2. If a straight line is passing through a point (c,0) on x-axis and parallel to y-axis, then the equation of the straight line is x = c

3. Equation of x-axis is y = 0.

(Because, the value of "y" in all the points on x-axis is zero)

4. Equation of y-axis is x = 0.

(Because, the value of "x" in all the points on y-axis is zero)

5. General equation of a straight line is

ax + by + c = 0

After having gone through above stuff, we hope that students would have understood the stuff "Intercept form equation of a line".

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