Answer:
[tex]slope=-3\\b=4\\[/tex]
Equation of the line
[tex]y=-3x+4[/tex]
Step-by-step explanation:
To find the slope we need two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] In this case we have the points [tex](0,4)[/tex] and [tex](2, -2)[/tex]
[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] (1)
We replace the points in the equation (1)
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{-2-4}{2-0} =\frac{-6}{2} =-3[/tex]
We know the equation of the line:
[tex]y=mx+b[/tex] (2)
To find b we replace the slope, x and y with one of the points in the equation (2)
[tex]4=-3*0+b\\4=0+b\\b=4[/tex]
We substitute m and b in the general equation of the line
[tex]y=-3x+4[/tex]
