Answer :
Given:
Two points on a line are A(11, - 1) and B(13, 3).
To find:
The point slope form of the line.
Solution:
Point slope form: If a line passes through two points [tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex], then the point slope form of the line is
[tex]y-y_1=m(x-x_1)[/tex]
where, m is slope, i.e., [tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex].
Two points on a line are A(11, - 1) and B(13, 3). Slope of the line is
[tex]m=\dfrac{3-(-1)}{13-11}[/tex]
[tex]m=\dfrac{3+1}{2}[/tex]
[tex]m=\dfrac{4}{2}[/tex]
[tex]m=2[/tex]
The slope of the line is 2 and it passing through (11,-1). So, the point slope form is
[tex]y-(-1)=2(x-11)[/tex]
[tex]y+1=2(x-11)[/tex]
Therefore, the required point slope form is [tex]y+1=2(x-11)[/tex].