what is an equation of the line that passes through the points (6,2) and (7,1)?

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(6,2)$ and $(x_2,y_2)=(7,1)$. Then $m=\frac{1 - 2}{7 - 6}=\frac{-1}{1}=- 1$.

Step2: Use point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(6,2)$ and $m=-1$, we have $y - 2=-1(x - 6)$.

Step3: Simplify to slope - intercept form

Expand the right side: $y - 2=-x + 6$. Add 2 to both sides to get $y=-x+8$.

Answer:

$y=-x + 8$