Answer:
[tex]\huge\boxed{y-1=1(x-6)\to y=x-5}[/tex]
Step-by-step explanation:
[tex]\text{The point-slope form of an equation of a line:}\\\\y-y_1=m(x-x_1)\\\\m-\text{slope}\\(x_1,\ y_1)-\text{point on a line}\\\\\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\===========================[/tex]
[tex]\text{We have two points}\ (6,\ 1)\ \text{and}\ (7,\ 2).\\\\\text{Calculate the slope:}\\\\m=\dfrac{2-1}{7-6}=\dfrac{1}{1}=1\\\\\text{Put the value of the slope and coordinates of the point}\ (6,\ 1)\\\text{to the equation:}\\\\y-1=1(x-6)\\y-1=x-6\qquad\text{add 1 to both sides}\\y-1+1=x-6+1\\y=x-5[/tex]
