Question

A line passes through (2,-1) and (4,5). What answer is the equation of the line? -3x+5y=-13

Answer 1

The equation of the line passes through (2, -1) and (4, 5) is -3x + y = - 7 So, option 2 is correct.

Solution:

Given, two points are (2, -1) and (4, 5)

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.

So, slope of line "m" is given as:

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

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

So slope of our line = $\frac{5-(-1)}{4-2}=\frac{5+1}{2}=3$

Now, let us find the line equation using point slope form:

$y-y_{1}=m\left(x-x_{1}\right) \text { where } m \text { is slope and }\left(x_{1}, y_{1}\right) \text { is point on the line. }$

Then equation of line is,

y – 5 = 3(x – 4)  

y – 5 = 3x – 12  

-3x + y = 5 – 12  

-3x + y = -7

Hence, the line equation is -3x + y = - 7 so, option 2 is correct.