Answer: Equation of line = [tex]y=-4x+9[/tex]
The slope of the line that contains the points (4, −7) and (1, 5) is -4 .
Step-by-step explanation:
The slope of a line that contains two points (a,b) and (c,d) is given by :-
[tex]m=\dfrac{d-b}{c-a}[/tex]
The slope of a line passing through (4, −7) and (1, 5) will be:_
[tex]m=\dfrac{5-(-7)}{1-4}\\\\\Rightarrow\ m=\dfrac{5+7}{-3}\\\\\Rightarrow\ m=\dfrac{12}{-3}\\\\\Rightarrow\ m=-4[/tex]
The equation of a line passing through (a,b) and has slope m is given by :_
[tex](y-b)=m(x-a)[/tex]
Then , the equation passing through (1,5) and has slope -4 will be
[tex](y-5)=-4(x-1)\\\\\Rightarrow\ y-5=-4x+4\\\\\Rightarrow\ y=-4x+4+5\\\\\Rightarrow\ y=-4x+9[/tex]
Hence, the equation of line = [tex]y=-4x+9[/tex]
The slope of the line that contains the points (4, −7) and (1, 5) is -4.
