Question

What is an equation of the line that passes through the points (6, 1)(6,1) and (7, 2)(7,2)? Put your answer in fully reduced form.

Answer 1

`\huge\boxed{y-1=1(x-6)\to y=x-5}`

Explanation:

`\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=(y_2-y_1)/(x_2-x_1)\\===========================`

`\text{We have two points}\ (6,\ 1)\ \text{and}\ (7,\ 2).\\\\\text{Calculate the slope:}\\\\m=(2-1)/(7-6)=(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`