AP Algebra 1 Honors

Question

performance task; suppose a line contains the points (0,0) and (q,r). a-what happens to the slope of the line if q and r are both tripled? b- suppose the horizontal and vertical distances from the origin to (q.r) were originally measured in inches. what happens to the slope of the line if these distances are measured again in centimeters? c-make a generalization about the effect of the unit of measurement on the slope of a line. please answer ASAP my teacher didnt teach us this topic!

Answer 1

The slope of the line containing the points (0,0) and (q,r) is:

 

m = (r-0)/(q-0) = r/q

 

If we triple q and r, the two points become (0,0) and (3q,3r).  So the slope is:

 

m = (3r-0)/(3q-0) = 3r/3q = r/q

 

Looks the same to me.

 

It doesn't matter if we change the units of distance from inches to centimeters or even to furlongs.  The slope is a ratio of distances, and the ratio stays the same regardless of the units used to measure the distances.