# What is the equation of the line between (0,2) and (23,0)?

Aug 8, 2018

$y = \left(\frac{2}{23}\right) x + 2$

#### Explanation:

I will solve for slope intercept form, $y = m x + b$

To find the equation given two points, I would use the slope formula to find the slope first

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{0 - - 2}{23 - 0} = \frac{2}{23}$

You do not have to find $b$ because it is the $y$-intercept, which we already know is $\left(0 , 2\right)$

$y = \left(\frac{2}{23}\right) x + 2$

Aug 9, 2018

color(indigo)(2x - 23y = 46, " is the equation in standard form"

#### Explanation:

$A \left(0 , 2\right) , B \left(23 , 0\right)$

Equation of $\overline{A B}$ is given by the formula

$\frac{y - {y}_{a}}{{y}_{b} - {y}_{a}} = \frac{x - {x}_{a}}{{x}_{b} - {x}_{a}}$

$\frac{y - 2}{0 - 2} = \frac{x - 0}{23 - 0}$

$\frac{y - 2}{-} 2 = \frac{x}{23}$

$23 y - 46 = - 2 x , \text{ Cross multiplying,}$

color(indigo)(2x - 23y = 46, " is the equation in standard form"