Grade 10 Math · Speed is a slope
The chapter's best secret
score 0

The chapter's best secret

Here it is, the chapter's best secret: on a distance–time graph, the slope IS the speed. Rise is kilometres gained, run is hours spent, so rise over run comes out in kilometres per hour. A steeper line is simply a faster trip — you can rank three cyclists at a glance without computing a thing.

The formula is the slope formula on wheels: v=dtv = \dfrac{d}{t} — read aloud, v equals d over t — where dd is the distance travelled (kilometres), tt is the time it took (hours), and vv is the speed that comes out, in km/h. Rearranged for whichever piece is hiding: d=vtd = vt (a speed held for a time covers ground) and t=dvt = \dfrac{d}{v} (the trip divided by your pace). Keep the units matched — kilometres with hours — and the answers come out as clean as the draws in this lesson.