**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.

**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

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

**
(y-y _{1})=m(x-x_{1}),**

Where, m=slope and

(x_{1},y_{1} ) are the points that lies on the line.

**Slope form:**

Slope m=
(y_{2}-y_{1})/(x_{2}-x_{1})

**
Or**

** **
m= (y_{1}-y_{2})/(x_{1}-x_{2})

Where (x_{1}, y_{1}) and (x_{2,} y_{2}) are the two point’s lies on the line.

1. Parallel lines have equal slope.

(That is if m_{1} is slope of line1 and m_{2} is slope of line2, then m_{1}=m_{2})

2. Perpendicular lines have negative reciprocal slopes.

(That is if m_{1} is slope of line1 and m_{2} is slope of line2, then m_{1}=-1/m_{2})

**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
m_{1}=4

The
slope of the second equation is m_{2}=4

m_{1}=m_{2}=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
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```
b = y-intercept.
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So, x-intercept = 8
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```
y-intercept = 5
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