Question

What is the point-slope form and standard form of (3,1) and (4, 2)?

Answer 1

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:

$\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text { where, }\left(x_{1}, y_{1}\right) \text { and }\left(x_{2}, y_{2}\right) \text { are two points on line. }$

$\text { Here } x_{1}=3 \text { and } y_{1}=1 \text { and } x_{2}=4 \text { and } y_{2}=2$

$\mathrm{m}=\frac{2-1}{4-3}=\frac{1}{1}=1$

The point slope form is given as:

$y-y_{1}=m\left(x-x_{1}\right)$

$\text { where } m \text { is slope and }(x_1, y_1) \text { is point on the line. }$

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