what is an equation of the line that passes through the points (6, -1) and (1, 4)?

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(6,-1)$ and $(x_2,y_2)=(1,4)$. Then $m=\frac{4-(-1)}{1 - 6}=\frac{4 + 1}{1-6}=\frac{5}{-5}=-1$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. We can use the point $(1,4)$ and $m=-1$. So $y - 4=-1(x - 1)$.

Step3: Simplify the equation

Expand the right - hand side: $y-4=-x + 1$. Add 4 to both sides to get the slope - intercept form $y=-x+5$.

Answer:

$y=-x + 5$