The slope intercept form of the line is given by: [tex]y = mx + b [/tex] The point-slope form is given by: [tex]y-yo = m (x-xo) [/tex] Where, m: slope of the line b: cutting point with the y axis (xo, yo): ordered pair that belongs to the line For line A: The slope is [tex]m = \frac{1-3}{4-1} [/tex] [tex]m = \frac{-2}{3} [/tex] The cut point with the y axis is: [tex]b = \frac{11}{3} [/tex] Substituting values we have: [tex]y = -\frac{2}{3}x + \frac{11}{3} [/tex]
For line B: The slope is given by: [tex]m=\frac{1-(-5)}{4-0}[/tex] [tex]m=\frac{1+5}{4}[/tex] [tex]m=\frac{6}{4}[/tex] [tex]m=\frac{3}{2}[/tex] Then, the equation of the line is: [tex]y-1= \frac{3}{2}(x-4) [/tex]
