What is a Straight Line?

A line is simply an object in geometry that is characterized under zero width object that extends on both sides. A straight line is just a line with no curves. So, a line that extends to both sides till infinity and has no curves is called a straight line.

Equation of a straight line:

y=mx+c

Where, y= how far up

x=how far along

m=slope or gradient

c= y intercept

This is the slope intercept form of the straight line equation, and it is the easiest equation for a straight line.

How do you find m and c?

c= where the line crosses the y axis.

m=slope.

m=change in x / change in y

Equation of a line with 2 points:(y-y1)=m(x-x1)

Where, m=(y-y_{1})/(x-x_{1})

Where, m= slope

For example:

Quest: Find the equation of the lines that passes through the points (-2,4) and (1,2)

Sol:

Now I have a slope and two points. I can find the equation (by solving first for “b”) if I have a point and the slope. So I need to choose one of the points and use it to solve for b. Using the point (â€“2, 4), I get:

y = mx + b

4 = (â€“ 2/3)(â€“2) + b

4 = 4/3 + b

4 â€“ 4/3 = b

12/3 â€“ 4/3 = b

b = 8/3

so,Â y = ( â€“ 2/3 ) x + 8/3.

On the other hand, if I use the point (1, 2), I get:

y = mx + b

2 = (â€“ 2/3)(1) + b

2 = â€“ 2/3 + b

2 + 2/3 = b

6/3 + 2/3 = b

b = 8/3

So it doesn’t matter which point I choose. Either way, the answer is the same:

y = (â€“ 2/3)x + 8/3

Straight lines can be more easily explained with the help of 3D air projection being used in Byjus application. As geometry proceeds, it gets more complicated and challenging for students to visualize things. So, it gets easier if these things are explained using proper visualization techniques. Students can also have a look at the demo videos available on youtube.

To learn more about Straight Lines you can click on this link for NCERT Solutions for Straight Lines