Respuesta :
ANSWER:
The line equation that passes through the given points (0,1) (-7,-5) is 6x – 7y + 7 = 0.
SOLUTION:
Given, two points are A(0, 1) and B(-7, -5).
We need to find the line equation that passes through the given two points.
We know that, general equation of a line passing through two points [tex]$\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right),\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)$[/tex] is given by
[tex]$y-y_{1}=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)\left(x-x_{1}\right)$[/tex] --- 1
Here,in our problem [tex]\mathrm{x}_{1}=0, \mathrm{y}_{1}=1, \mathrm{x}_{2}=-7$ and $\mathrm{y}_{2}=-5$[/tex]
Now substitute the values in (1)
[tex]$y-1=\left(\frac{-5-1}{-7-0}\right)(x-0)$[/tex]
[tex]$y-1=\frac{-6}{-7}(x)$[/tex]
[tex]$y-1=\frac{6}{7} x$[/tex]
7y – 7 = 6x
6x – 7y + 7 = 0
Hence, the line equation that passes through the given points is 6x – 7y + 7 = 0.
