Question

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

Answer 1

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


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