# Learning Intercept Form

Introduction to Learning  intercept  form:

Slope:

An area of surface that tends evenly towards top or down is called as slope. The slope is also called as gradient. The slope of a line  containing the x and y axes is generally represented by  m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

## Learning Intercept form :

Slope form:

The equation of the line can be expressed as the following forms,

Slope Intercept form:

Y=mx+b,

Where ,

m=slope

b=Y-intercept

```           An equation for a line with nonzero x-intercepts and
```
```y-intercepts can be written as:
```
```                        x/a + y/b = 1
```
```          where , a = x-intercept
```
```                     b = y-intercept.
```
``` This is called the intercept form of the equation of a line.
```

Learning Point slope form:

(y-y1)=m(x-x1),

Where, m=slope and

(x1,y1 ) are the points that lies on the line.

Slope form:

Slope m= (y2-y1)/(x2-x1)

Or

m= (y1-y2)/(x1-x2)

Where (x1, y1) and (x2, y2) are the two point’s lies on the line.

## learning intercept form- Slope of Parallel and Perpendicular intercept lines:

1. Parallel lines have equal slope.

(That is if m1 is slope of line1 and m2 is slope of line2, then    m1=m2)

2. Perpendicular lines have negative reciprocal slopes.

(That is if m1 is slope of line1 and m2 is slope of line2, then m1=-1/m2)

Learning - Sample slope intercept form problems:

1. Find the slope of the equation y=4x-3

Solution:

Y=4x-3

It is in the slope intercept  form y=mx+b.

So slope of the given equation m= 4

2. Find the slope- intercept  of the equation 3y=6x-12

Solution:

3y=6x-12

Divide by 3 on both sides,

Y=2x-4

So slope –intercept of the given equation b= -4

3. Find the slope -y=3x+7

Solution:

-y=3x+7

Divide by -1 on both sides,

Y=-3x-7

So slope of the given equation b= -7

4. Verify the below equations are parallel.

4y=16x+12

Y=4x+8

Divide by 4 on both sides,

Y=4x+3

Slope m1=4

The slope of the second equation is m2=4

m1=m2=4

So both equations are parallel.

5.find the intercept of the given equation : x / 8 + y / 5 = 1

Solution:

```             x/a + y/b = 1
```
```    where , a = x-intercept
```
```               b = y-intercept.
```
```         So, x-intercept   = 8
```
```               y-intercept   = 5
```