## How does using the point slope form of a linear equation make it easier to write the equation of a line?

October 11, 2019// Blog//

We’ve got a line with the slope 2. One of the points that the line passes through has got the coordinates (3, 5). It’s possible to write an equation relating x and y using the slope formula with

(x1,y1)=(3,5)and(x2,y2)=(x,y)

(x1,y1)=(3,5)and(x2,y2)=(x,y)

m=y2−y1x2−x1

m=y2−y1x2−x1

2=y−5x−3

2=y−5x−3

2⋅(x−3)=(y−5)⋅(x−3)x−3

2⋅(x−3)=(y−5)⋅(x−3)x−3

2(x−3)=y−5

2(x−3)=y−5

Since we used the coordinates of one known point and the slope to write this form of equation it is called the point-slop form

y−y1=m(x−x1)

y−y1=m(x−x1)

Another way of writing linear equations is to use the standard form

Ax+By=C

Ax+By=C

Where A, B and C are real numbers and where A and B are not both zero.

Since the slope of a vertical line is undefined you can’t write the equation of a vertical line using neither the slope-intersect form or the point-slope form. But you can express it using the standard form.