Answer:
The equation is [tex]3x -y =7[/tex]
Solution:
Let us assume that the [tex](x_1, y_1) = (4,5)[/tex] and [tex](x_2, y_2) = (2,-1)[/tex]
The slope of the line m is [tex]=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-5}{2-4}=\left(\frac{6}{2}\right)=3[/tex]
We know the equation of a line at a given point [tex](x_1,y_1) is (y-y_1) = m(x-x_1)[/tex]
Let me take the point (4,5) here,
So the equation of the line is
[tex](y-5)=3 \times(x-4)[/tex]
[tex]y-5=3 x-12[/tex]
[tex]3x-12 - y+5 = 0[/tex]
[tex]3x -y -7 =0[/tex]
[tex]3x -y =7[/tex]
So, the equation is [tex]3x-y =7[/tex]
