Question

Write the slope intercept form through: (5,1) and(2, -2)

Answer 1

We see that the slope of this line is $\frac{-2-1}{2-5}=1,$ so we plug this and the point $(5,1)$ into the point-slope form $y-y_1=m(x-x_1)$ (note that there's nothing special about the point I picked; you can choose any point on the line):

$y-1=x-5.$ This rearranges to the slope-intercept form $\boxed{y=x-4}.$