Question

PLEASE HELP!

A and B are points on a line that has the slope –3. The abscissa of B exceeds the abscissa of A by 2. State the relationship of the ordinate of B to the ordinate of A.

Answer 1

bearing in mind that abscissa is another name for the x-coordinate and ordinate is another name for the y-coordinate.

let's say we have two points A and B, and their abscissa and ordinate are A(x1,y1) B(x2,y2).

we know that x2 is larger than x1 by 2, namely their difference yields 2, thus x2 - x1 = 2, we also know that the slope of that segment with those two points is -3.

`\bf (\stackrel{x_1}{x1}~,~\stackrel{y_1}{y1})\qquad (\stackrel{x_2}{x2}~,~\stackrel{y_2}{y2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{y2}-\stackrel{y1}{y1}}}{\underset{run} {\underset{x_2}{x2}-\underset{x_1}{x1}}}~~=~~\stackrel{\stackrel{slope}{\downarrow }}{-3}\implies \cfrac{y2-y1}{2}=-3\implies y2-y1=-6 \\\\\\ y2=y1-6\qquad \impliedby \textit{the ordinate of B is 6 less than the ordinate of A}`