The equation of the line is y = -x + 5.
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To find the equation of the line with given two points that lie on the line, we will use:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Choose:
[tex](x_1,y_1)=(2,3) \quad \quad \quad (x_2,y_2)=(4,1)[/tex]
Substitute the coordinates of the points to the equation
[tex]\displaystyle y-3=\frac{1-3}{4-2}(x-2)[/tex]
[tex]\displaystyle y-3=\frac{-2}{2}(x-2)[/tex]
[tex]y-3=-1(x-2)[/tex]
[tex]y-3=-x+2[/tex]
Isolate [tex] y [/tex] by transposing -3 to the other side.
[tex]y=-x+2+3[/tex]
[tex]\boxed{y=-x+5}[/tex]
Therefore, the equation of the line is y = -x + 5
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Hope it helps.
