Chapter 4 - Writing Linear Functions - 4.2 - Writing Equations in Point-Slope Form - Exploration - Page 181: 2

$m=\frac{y-y_1}{x-x_1}$ $y-y_1=m(x-x_1)$

Write slope formula using the given points $(x_1,y_1)$ and $(x,y)$: $$m=\frac{y-y_1}{x-x_1}$$ Multiply both sides by $x-x_1$: $$m(x-x_1)=y-y_1$$ Swap the sides: $$y-y_1=m(x-x_1)$$ So, point-slope form is obtained.