Question

Hello, I am having trouble understanding the "Point-slope form" in mathematics. If anyone could, please tell me its purpose and how I can use it in a math problem (an example would be nice). My school doesn't teach it very well :(.

Answer 1

what really helps is if you label your x and y

Answer 2

Let me think of an example

As the name suggests, it is useful when you are given a point...and a slope...and are asked to find the equation of a line with these characteristics

So say I give you a point (1,2) and a slope of 4

You would use the point slope formula *as @moonrose has shown above*

\[\large y - y_1 = m(x - x_1)\]

You would take that formula...and plug in the point I have given you and the slope

obviously, you need to know that a coordinate is made up of (x,y) so that point I gave you (1,2) will make

\(\large x_1\) = 1
and
\(\large y_1\) = 2

And also m = slope = 4 I gave

So you would turn your formula into

\[\large y - y_1 = m(x - x_1)\]
\[\large y - 2 = 4(x - 1)\]
\[\large y - 2 = 4x - 4\]
\[\large y = 4x - 2\]

This would be the equation of a line with a point (1,2) and with a slope of 4

Answer 3

thanks