Given:
[tex]The\text{ given points are \lparen-10,-20\rparen and \lparen1,-9\rparen.}[/tex]
Required:
We need to find the point-slope equation of the line that passes through the given points.
Explanation:
Consider the point-slope form of the equation.
[tex]y-y_1=m(x-x_1)[/tex]
Consider the slope formula.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]Substitute\text{ }y_2=-9,y_1=-20,x_2=1,\text{ and }x_1=-10\text{ in the slope formula.}[/tex][tex]m=\frac{-9-(-20)}{1-(-10)}[/tex][tex]m=\frac{-9+20}{1+10}[/tex][tex]m=\frac{11}{11}[/tex][tex]m=1[/tex]
Use the first point (-10,-20) in the point-slope equation.
[tex]Substitute\text{ }m=1,\text{ }x_1=-10,\text{ and }y_1=-20\text{ in the point-slope form of equation}[/tex]
[tex]y-(-20)=(1)(x-(-10))[/tex]
Final answer:
[tex]y-(-20)=(1)(x-(-10))[/tex]
