Question

Write an equation in point-slope form of the line through the given points. Then write the equation in slope-intercept form.

Answer 1

$y-y_1=m(x-x_1) \\ \\ m=-\frac{5}{8} \\ (-10,-6) \\ x_1=-10 \\ y_1=-6 \\ \Downarrow \\ y-(-6)=-\frac{5}{8}(x-(-10)) \\ \boxed{y+6=-\frac{5}{8}(x+10)} \ - \ \hbox{the point-slope form} \\ \\ y+6=-\frac{5}{8}(x+10) \\ y+6=-\frac{5}{8}x-\frac{50}{8} \\ y=-\frac{5}{8}x-\frac{50}{8}-6 \\ y=-\frac{5}{8}x-\frac{25}{4}-\frac{24}{4} \\ y=-\frac{5}{8}x-\frac{49}{4} \\ \boxed{y=-\frac{5}{8}x-12 \frac{1}{4}} \ - \ \hbox{the slope-intercept form}$