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:

`(y1 - y2)/(x1 - x2) = ( (- (2)/(3) ) - ( -2 ))/((1) - ( (1)/(2) ) ) = ( (4)/(3) )/( (1)/(2) ) \\ = (4)/(3) * (2)/(1) = (8)/(3)`
Therefore, the slope is 8/3.

To find b, we must plug in the slope and one point:

`(1) = ( (8)/(3) )( - (2)/(3) ) + b \\ 1 = - (16)/(9) + b \\ (25)/(9) = b`
Therefore, b is 25/9, and the total equation is

`y = (8)/(3) x + (25)/(9)`