The point-slope form and standard form of (3,1) and (4, 2) are y – 1 = x – 3 and x – y = 2 respectively
Solution:
Given, two points are (3, 1) and (4, 2)
We have to find that a line that passes through the given two points.
First let us find the slope of the line that passes through given two points.
Slope of line "m" is given as:
[tex]\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text { where, }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { are two points on line. }[/tex]
[tex]\text { Here } x_{1}=3 \text { and } y_{1}=1 \text { and } x_{2}=4 \text { and } y_{2}=2[/tex]
[tex]\mathrm{m}=\frac{2-1}{4-3}=\frac{1}{1}=1[/tex]
The point slope form is given as:
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]\text { where } m \text { is slope and }(x_1, y_1) \text { is point on the line. }[/tex]
y – 1 = 1(x – 3)
y - 1 = x - 3
Line equation in point slope form is y – 1 = x – 3 -- eqn 1
Now, line equation in standard form i.e. ax + by = c is found out by eqn 1
y – 1 = x – 3
x – y = 3 – 1
x – y = 2
Hence, the line equation in point slope form and standard forms are y – 1 = x – 3 and x – y = 2 respectively
