Solution:
The equation of line in point slope form is given as:
[tex]y - y_1 = m(x-x_1)[/tex]
Where, m is the slope of line
The slope of line is given as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
From given,
[tex](x_1, y_1) = (\frac{2}{5} , \frac{19}{20})\\\\(x_2, y_2) = (\frac{1}{3} , \frac{11}{12})[/tex]
Substituting the values we get,
[tex]m = \frac{\frac{11}{12} - \frac{19}{20}}{\frac{1}{3} - \frac{2}{5}}\\\\Simplify\\\\m = \frac{-8}{240} \times \frac{15}{-1}\\\\ m = \frac{120}{240}\\\\m = \frac{1}{2}[/tex]
[tex]\text{Substitute } m = \frac{1}{2} \text{ and } (x_1, y_1) = (\frac{2}{5} , \frac{19}{20}) \text{ in eqn 1 }[/tex]
[tex]y - \frac{19}{20} = \frac{1}{2}(x - \frac{2}{5})\\\\y - \frac{19}{20} = \frac{x}{2} - \frac{1}{5}\\\\\frac{x}{2} - y = - \frac{19}{20} + \frac{1}{5}\\\\\frac{x}{2} - y = \frac{-15}{20}\\\\Simplify\\\\y = \frac{1}{2}x + \frac{3}{4}[/tex]
In standard form,
[tex]y = \frac{4x+6}{8}\\\\8y = 4x + 6\\\\4x - 8y = -6[/tex]
Thus the equation of line is found
