Question

Determine the slope of the line that passes through each pair of points.

1.(5,1) and (2,7)
2.(5,3)and(-2,3)

Answer 1

`1.)\\\\(5,1) \ \ and \ \ (2,7)\\\\First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \\ \\ m= (y_(2)-y_(1))/(x_(2)-x_(1) ) \\ \\m=( 7-1)/(2-5) = (6)/(-3)=-2 \\ \\ Use \ point \ form \ of \ a \ line\ with \ one \ point: \\ \\ y-y_(1) =m(x-x _(1)) \\ \\m=-2 , \ \x_(1)=5, \ \ y_(1)=1 \\ \\y-1 = -2(x-5 ) \\\\y=-2x+10+1 \\ \\y=-2x+11`



`2.)\\\\(5,3)\ \ and \ \ (-2,3)\\\\First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \\ \\ m= (y_(2)-y_(1))/(x_(2)-x_(1) ) \\ \\m=( 3-3)/(-2-5) = (0)/(-7)=0\\ \\ Use \ point \ form \ of \ a \ line\ with \ one \ point: \\ \\ y-y_(1) =m(x-x _(1)) \\ \\m=0 , \ \x_(1)=5, \ \ y_(1)=3 \\ \\y-3 = 0\cdot (x-5 ) \\\\y-3=0 \\ \\y=3`