Question

What is the equation of the line passing through the points  (Two-fifths, StartFraction 19 Over 20 EndFraction)and  (one-third, StartFraction 11 Over 12 EndFraction) in slope-intercept form?​

Answer 1

Answer:

the line passing through the points (Two-fifths, StartFraction 19 Over 20 EndFraction (Two-fifths, StartFraction 19 Over 20 EndFraction)and (one-third, StartFraction 11 Over 12 EndFraction) in slope-intercept form?

Step-by-step explanation:

Answer 2

4x - 8y = -6 is the equation of line in standard form

Solution:

The equation of line in point slope form is given as:

$y - y_1 = m(x-x_1)$

Where, m is the slope of line

The slope of line is given as:

$m = \frac{y_2-y_1}{x_2-x_1}$

From given,

$(x_1, y_1) = (\frac{2}{5} , \frac{19}{20})\\\\(x_2, y_2) = (\frac{1}{3} , \frac{11}{12})$

Substituting the values we get,

$m = \frac{\frac{11}{12} - \frac{19}{20}}{\frac{1}{3} - \frac{2}{5}}\\\\Simplify\\\\m = \frac{-8}{240} \times \frac{15}{-1}\\\\ m = \frac{120}{240}\\\\m = \frac{1}{2}$

$\text{Substitute } m = \frac{1}{2} \text{ and } (x_1, y_1) = (\frac{2}{5} , \frac{19}{20}) \text{ in eqn 1 }$

$y - \frac{19}{20} = \frac{1}{2}(x - \frac{2}{5})\\\\y - \frac{19}{20} = \frac{x}{2} - \frac{1}{5}\\\\\frac{x}{2} - y = - \frac{19}{20} + \frac{1}{5}\\\\\frac{x}{2} - y = \frac{-15}{20}\\\\Simplify\\\\y = \frac{1}{2}x + \frac{3}{4}$

In standard form,

$y = \frac{4x+6}{8}\\\\8y = 4x + 6\\\\4x - 8y = -6$

Thus the equation of line is found