Question

Find the equation of the line passing through the points (-2/3,1) and (-2,1/2). Write the equation in standard form.

Answer 1

Standard form is y = mx + b.
To find the slope, m, we must find the 'rise over run,' or the difference in y divided by the difference in x. We do this by:
$\frac{y1 - y2}{x1 - x2} = \frac{ (- \frac{2}{3} ) - ( -2 )}{(1) - ( \frac{1}{2} ) } = \frac{ \frac{4}{3} }{ \frac{1}{2} } \\ = \frac{4}{3} \times \frac{2}{1} = \frac{8}{3}$
Therefore, the slope is 8/3.

To find b, we must plug in the slope and one point:
$(1) = ( \frac{8}{3} )( - \frac{2}{3} ) + b \\ 1 = - \frac{16}{9} + b \\ \frac{25}{9} = b$
Therefore, b is 25/9, and the total equation is
$y = \frac{8}{3} x + \frac{25}{9}$