Respuesta :
Part A
we can calculate the slope taking two points of the line and using the slope formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex]where (x2,y2) is a right point from (x1,y1)
i will use the points (8,32) and (12,24)
so replacing
[tex]\begin{gathered} m=\frac{24-32}{12-8} \\ \\ m=\frac{-8}{4}=-2 \end{gathered}[/tex]the slope is -2
Part B
to make the equation we use the general form of the line
[tex]y=mx+b[/tex]where m is the slope and b the y-intercept, we have the slope because s is the same line than HI
so m=-2
now replace the slope and a point on the general equation to find b
i will use the point (8,32)
[tex]\begin{gathered} (32)=(-2)(8)+b \\ 32=-16+b \\ b=32+16 \\ b=48 \end{gathered}[/tex]now we can rewrite the equation replacing b=48 and m=-2
the equation is
[tex]y=-2x+48[/tex]