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

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Answer 1 · 2018-08-08T22:46:56

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

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

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

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $m=(y_2-y_1)/(x_2-x_1)$

$m = \frac{0 - - 2}{23 - 0} = \frac{2}{23}$ $m=(0--2)/(23-0)=2/23$

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

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

Answer 2 · 2018-08-09T10:42:53

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

$A (0, 2), B (23, 0)$ $A (0, 2), B (23, 0)$

Equation of $¯ ¯¯¯¯ ¯ A B$ $bar(AB)$ is given by the formula

$\frac{y - y_{a}}{y_{b} - y_{a}} = \frac{x - x_{a}}{x_{b} - x_{a}}$ $(y - y_a) / (y_b - y_a) = (x - x_a) / (x_b- x_a)$

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

$\frac{y - 2}{- 2} = \frac{x}{23}$ $(y-2) / -2 = x / 23$

$23 y - 46 = - 2 x, Cross multiplying,$ $23y - 46 = -2x, " Cross multiplying,"$

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

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