GRAPHS ON THE GO : Sketching a straight line.

Knowing how to sketch straight lines is very important if belong Mathematics and Science.

How to sketch straight lines?

The standard equation of a straight line is ax + by + c = 0

There are basic 5 forms of line's equation.

In order to understand all the five we must know some of the basic terms we will be frequently using-

Slope of a line: Slope of a line defines the tangent(tan of trigonometry) of the angle at which the line is inclined with the +ve x axis.

    

Above mentioned are three ways to find the slope of a line. slope is generally represented by m.

                                                                         

Y-intercept: 

The intercept cut by the line with y axis. It is represented by c.

Let's come back to the 5 forms of equation of line-

1. One point slope form

2. Two point slope form

3. Slope intercept form

4. Intercept form

5. Normal form

1. One point slope form: 

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

In this we need one point (x1,y1) and slope of the line.

2. Two point slope form: It is the modified form of the first form -

In this we need two points (x1,y1) and (x2,y2).

Here we replace slope in above form as (y2-y1)/(x2-x1)

and one point.

and the general form results out to be-

(y-y1) = ((y2-y1)/(x2-x1))(x-x1)

3. Slope intercept form

In this we need slope(m) and y-intercept(c)

The general form results out to be-

y = mx + c

4. Intercept form: In this form we just need x-intercept and y-intercept.

Easiest way to find the intercept of any function is that-

put x=0 and y obtained will be your y-intercept                        

put y=0 and x obtained will be your x-intercept.

But if your know both intercepts and lets say 

x-intercept is a and y intercept is b, 

then equation in this form is given as-

(x/a) + (y/b) = 1

5. Normal form: It is given by -

xcos(a) + ysin(a) = p

SKETCHING THE EQUATION OF LINE OBTAINED-

After you have successfully created the equation of the straight line then next work comes which is to plot the line on graph, below mentioned are steps which are easiest you can follow in order to plot the straight-

1. put x=0 and find y.

2. locate point obtained.

3. put y=0 and find x.

4. plot the point obtained.

5. join these two points.

6. You get the line required to plotted.

OR

1. Try to convert the equation into intercept form.

2. Now plot according to the intercepts obtained.

                 

                                                                       

Stay Tuned for the next post.

For any query comment down there.

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