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.